30% of all cars undergoing a headlight inspection failed the inspection by JPJ and a random sample of 400 cars were selected. Using normal approximation of Binomial distribution, find the value of k if the probability that less P(X<100) ≈ P| Z≤. = P(Z < = 99.5-120 k than 100 cars failed the inspection given as O a. 0.3 O b. 9.16 O c. 84 O d. 400
Q: The amount of syrup that people put on their pancakes is normally distributed with mean 62 mL and…
A: Formula : Z =(X - μ)/σ
Q: The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 70…
A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…
Q: According to a study done by UCB students, the height for Martian adult males is normally…
A: a. Consider that the mean and standard deviation of a random variable X are µ and σ, respectively.…
Q: The number of calories consumed by customers at the Chinese buffet is normally distributed with mear…
A: The mean is 2784 and the standard deviation is 617.
Q: The average teacher's salary in North Dakota is $35,441 . Assume a normal distribution with…
A: Given Mean=35441, standard deviations=5100, n=60
Q: Q2: According to the American Automobile Association (AAA), the average cost of a gallon of regular…
A: The question is about sampling dist. Given : Popl. mean cost of a gallon of regular unleaded fuel (…
Q: Suppose that the weight of seedless watermelons is normally distributed with mean 6.6 kg. and…
A: Given Mean = 6.6 Standard deviation = 1.8kg x is normal distribution
Q: The probability of failure p of a resistor is 0.08. Assuming binomial distribution, what is the…
A: a)Let p be the probability of failure of a resistor.X be the number of failure of a resistor…
Q: Let X represent the full height of a certain species of tree. Assume that X has a normal probability…
A: Given that, Mean = 243.5 Standard deviation = 58.6 Sample size = 160
Q: Assume the random variable X is normally distributed with mean u = 50 and standard deviation o = 7.…
A:
Q: What is the probability that the average of the 50 samples exceeds 7 minutes? (Hint: std. dev. of 0…
A: Here Given μ=8 Minutes σ=8 Minutes n=50
Q: A company advertises that the batteries it sells is normally distributed with a mean life of 25…
A:
Q: The probability that the sample mean of a random variable X is more than 1.96 standard deviations…
A: We have to find correct answer..
Q: Refer to the accompanying table, which describes results from groups of 8 births from 8 different…
A: Mean(μ)=E(X)=∑X.P(X)E(X2)=∑x2.P(X)variance(σ2)=E(X2)-E(X)2Standard deviation(σ)=E(X2)-E(X)2
Q: the sape of the distribution of the time required to get an oil change at a 10-minute oil change…
A: Answer: Given,n=40 Mean=11.4 Standard deviation =3.2
Q: The probability that a randomly selected adult has an IQ less than 128 is (Type an integer or…
A: Given: Consider X as a random variable that follows a normal distribution with mean 22 and…
Q: ariance of a Binomial Distribution with number of trials as 12 and probability of success being 1/3…
A: Variance of a Binomial Distribution with number of trials as 12 and probability of success being 1/3…
Q: A production line in a factory, assembles laptops. A random sample of assembly time of 36 laptops…
A: Given n=36 Mean=25 Standard deviation=6
Q: Let X represent the full height of a certain species of tree. Assume that X has a normal probability…
A: We want to find mean and standard deviations of the sample mean.
Q: The times for a particular journey during rush hour in a large city have to mean 24.4 minutes and…
A: The variable is the time for a particular journey during rush hour in a large city. It is given…
Q: Suppose 100 independent random x values are each distributed N(1,9) – normal distribution with a…
A: Given that. X~N( 1 ,9) μ=1 , ?=3 Z-score =( x - μ )/? NOTE:- According to bartleby…
Q: suppose that the weight of seedless watermelons is normally distributed with mean 7 kg. and standard…
A:
Q: is less than 68 inch or greater than 70 inch? 5. Choose a person at random and give him or her an IQ…
A: Consider a random variable X which, follows normal distribution, indicates the IQ scores. The mean…
Q: A random sample of size 625 was selected from a large population with population mean ? = 15 and…
A:
Q: Q2] As shown in the table below that gives the age distribution of individuals starting new…
A: Given R = 30, The age frequency table is as follows.
Q: 4. Suppose only 40% of all drivers in Florida regularly wear a seatbelt. A random sample of 500…
A:
Q: he following histograms each represent binomial distributions. Each distribution has the same number…
A: The objective of the question is to match the given probabilities of success (p=0.4, p=0.5, p=0.6)…
Q: Let X represent the full height of a certain species of tree. Assume that X has a normal probability…
A: We want to find the meana nd variance of sample mean.
Q: In a recent survey, approximately 90% of U.S. adults own a cell phone. Let's assume this can be…
A: Given Information : In a recent study , approximately 90% of US adults own a cell phone . Lets…
Q: Let Z denote the standard normal random variable, ?(−.54<?≤.78)is closest to
A:
Q: The mean daily production of a herd of cows is assumed to be normally distributed with a mean of 38…
A: Given data,normal distributionμ=38σ=8.7
Q: What is the distribution of X? X ~ N( , ) b. Find the probability that the person is between 66.6…
A:
Q: Let X represent the full height of a certain species of tree. Assume that X has a normal probability…
A: given data normal distribution μ = 32.3σ = 73.6n = 37
Q: The temperature in degrees Celsius at a certain location is normally distributed with a mean of 68…
A:
Q: As shown in the table below that gives the age distribution of individuals starting university…
A: Given information: The data represents the continuous frequency distribution of ages.
Q: The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean…
A: given data, normal distribution x = no of caleries that custmor consumesμ=2747σ=619we have to find…
Q: The average height of adult males in the United States is 68.5 inches. Assume that a = 3.1 inches…
A: Given,sample size(n)=15mean(μ)=68.5standard deviation(σ)=3.1
Q: Find the probability that a randomly selected adult has an IQ between 91 and 119.
A: Let X denote the IQ scores of the adults. Given that X follows N(mean = 105, SD = 15), then Z = (X…
Q: Suppose that the speed at which cars go on the freeway is normally distributed with mean 71 mph and…
A:
Q: Suppose that the speed at which cars go on the freeway is normally distributed with mean 76 mph and…
A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…
Q: |Q3. Expected value, variance and the mgf of the sample mean Let X1,..., X, be independent and…
A: Ans:
Q: Let XX represent the full height of a certain species of tree. Assume that XX has a normal…
A: Given: XX~N(μ,σ) (Population mean) μ = 8.2ft, σ=38.8ft, sample size (n) = 83 trees…
Q: The number of calories consumed by customers at the Chinese buffet is normally distributed with mean…
A:
Q: For a binomial distribution with p.10 and n = 100, what is the z-score corresponding to X = 16? 06…
A: We shall find the z score of binomial distribution. We shall state the formula also. Please see the…
Step by step
Solved in 2 steps
- The amount of syrup that people put on their pancakes is normally distributed with mean 61 mL and standard deviation 8 mL. Suppose that 49 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X N( 61 b. What is the distribution of ? N( 61 49 c. If a single randomly selected individual is observed, find the probability that this person consumes is between 60 mL and 61.3 mL. 0.0657 d. For the group of 49 pancake eaters, find the probability that the average amount of syrup is between 60 mL and 61.3 mL. | 0.4338 e. For part d), is the assumption that the distribution is normal necessary? YesO No o[4+2=6 pts] The following table gives the distribution of the number of hours students study each day (X) in a certain university. 1 3 4 P(X) 0.15 0.25 0.30 0.20 0.10 a) Find the mean and standard deviation of the number of hours of study. b) If 6 students are selected from this university, what is the probability that 4 will be found to study 3 hours each day?The number of ants per acre in the forest is normally distributed with mean 44,000 and standard deviation 12,192. Let X = number of ants in a randomly selected acre of the forest. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( 44,000 12,192 b. Find the probability that a randomly selected acre in the forest has fewer than 47,638 ants. c. Find the probability that a randomly selected acre has between 45,935 and 56,143 ants. d. Find the first quartile. ants (round your answer to a whole number)
- A. The average number of miles (in thousands) that a car's tire will function before needing replacement is 66 and the standard deviation is 11. Suppose that 43 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution. Is the assumption that the distribution is normal necessary? For the 43 tires tested, find the probability that the average miles (in thousands) before the need for replacement is between 68.4 and 70.2 B. CNNBC recently reported that the mean annual cost of auto insurance is 1050 dollars. Assume the standard deviation is 230 dollars, and the cost is normally distributed. You take a simple random sample of 17 auto insurance policies. Round your answers to 4 decimal places. Is the assumption that the distribution is normal necessary? 1.A simple random sample of 17 auto insurance policies, find the probability that the average cost is more than $1065 C. Suppose the age that children learn to walk is…The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2650 and standard deviation 634. One randomly selected customer is observed to see how many calories X that customer consumes. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that the customer consumes less than 2530 calories. c. What proportion of the customers consume over 3010 calories? d. The Piggy award will given out to the 2% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award? calories. (Round to the nearest calorie)The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2941 and standard deviation 556. One randomly selected customer is observed to see how many calories X that customer consumes. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that the customer consumes less than 2574 calories. c. What proportion of the customers consume over 3160 calories? d. The Piggy award will given out to the 2% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award? calories. (Round to the nearest calorie)
- Suppose that the speed at which cars go on the freeway is normally distributed with mean 66 mph and standard deviation 5 miles per hour. Let X be the speed for a randomly selected car.a. What is the distribution of X? X ~ N( ________ , ________)b. If one car is randomly chosen, find the probability that it is traveling more than 62 mph. Round to 4 decumal places. c. If one of the cars is randomly chosen, find the probability that it is traveling between 68 and 71 mph. Round to 4 decimal places.The number of calories consumed by customers at the Chinese buffet is normally distributed with mean 2987 and standard deviation 509. One randomly selected customer is observed to see how many calories X that customer consumes. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N( ? , ? )b. Find the probability that the customer consumes fewer than 2608 calories. c. What proportion of the customers consumed more than 3240 calories?A production line in a factory, assembles laptops. A random sample of assembly time of 36 laptops has been drawn from this factory. Suppose, the population distribution has a mean assembly time of 25 minutes and standard deviation 6 minutes. What is the probability that a sample mean is 26 minutes? Select one: O'O E b. =P(Z>1) C. =P(Z=o) d. =P(Z<1) e. None of the others ge Next page
- he lengths of adult mates' hands are normally distributed with mean 185 mm and standard eviation is 7.5 mm. Suppose that 47 individuals are randomly chosen. Round all answers to 4 vhere possible. a. What is the distribution of ¤? ¤ ~ N( 185 X) oe oe 1.094 b. For the group of 47, find the probability that the average hand length is less than 184. 0.6357 x G Find the first quartile for the average adult male hand length for this sample size.According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 67 inches and a standard deviation of 2.5 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X N( 67 2.5 b. Find the probability that the person is between 65.5 and 68,9 inches. -0.5021 c. The middle 50% of Martian heights lie between what two numbers? Low: inches High: inchesQ2] As shown in the table below that gives the age distribution of individuals starting new university employments. Find the following probabilities: 1-Ages (28-39). 2- Age>55. 3-Age<35. N:15 G:2 R=30 15-24 25-34 35-44 45-54 320-R 420+R| 315 55-64 Age Frequency 65-74 120 250 220-R
