2. a. The Intelligence Quotient (IQ) of adults is approximately normally distributed with mean 100 and standard deviation 15. i. Find the probability that a random sample of 100 adults will have a mean IQ greater than 104. ii. Find the sample size n, given that the probability that the mean IQ exceeds 101 is 0.031.
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- The Boeing 157-200 ER aircraft carries 200 passengers and has doors with a height of 72 inches. Male heights are normally distributed with a mean of 67.4 inches and a standard deviation of 3.8 inches. 1. If a male passenger is selected at random, find the probability that he can pass through the door without leaning over. Enter your answer to four decimal places. 2. If half of the 200 passengers are men, find the probability that the average height of the 100 men is less than 72 inches. Enter your answer to four decimal places.Suppose that the distribution of the grades of students in MAPEH performance 1 is roughly normally distributed with a mean of 85 and a standard deviation of 5 a. Between what values do we expect the grades of the middle 68% of the MAPEH students in performance 1 lie? b. Suppose you randomly select 16 MAPEH students, find the probability that the average grades of these students is at least 86. c. A MAPEH student whose grades lies in the upper 1% of the distribution (inclusive of the 1% cutoff) is considered extremely performing in Performance 1. Can you say that Jazzer, a randomly selected student who obtained a grade of 95, is one of those who performed extremely in Performance 1?Provide an original example of some practical case where we can use the normal distribution (e.g., IQ scores follow a normal distribution of probabilities with a mean IQ of 100 and a standard deviation of 15 IQ points.). Assign your numbers for mean 70 and standard deviation 30. Make sure 70 is about four times bigger than 30. Then select any number 90 below or above mean 70, but not too far from 70. Find following two probabilities: 1) P(x < a)2) P(x > a)Use the formula z = (a - μ)/σ to calculate your z-value. Please refer to the Appendix Table for the Standard Normal Distribution Hint: To find P(x>a) use formula: P(x>a) = 1 - P(x<a). Describe how to would find P( 65 < x < 25). Provide an original example to illustrate how to find such probabilities.
- The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2808 and standard deviation 571. One randomly selected customer is observed to see how many calories X that customer consumes. Round all answers to 4 decimal places where possible. b. Find the probability that the customer consumes less than 2436 calories. c. What proportion of the customers consume over 3047 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 2801 and standard deviation 544. One randomly selected customer is observed to see how many calories X that customer consumes. Round all answers to 4 decimal places where possible. b. Find the probability that the customer consumes less than 2648 calories. c. What proportion of the customers consume over 3123 calories? d. The Piggy award will given out to the 1% 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)Assume that adults have IQ scores that are normally distributed with a mean of95.4 and a standard deviation of 16.6. Find the probability that a randomly selected adult has an IQ greater than 118.1 The probability that a randomly selected adult from this group has an IQ greater than 118.1 is what?
- From a sample with n = 12, the mean number of televisions per household is 2 with a standard deviation of 1 television. Using Chebychev's Theorem, determine at least how many of the households have between 0 and 4 televisions. At least of the households have between 0 and 4 televisions. (Simplify your answer.)6. Assume that cans of Coke are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of 0.11 oz. a. Find the probability that a single can of Coke has at least 12.19 oz. b. Find the probability that a pack of 36 cans of Coke have a mean of at least 12.19 oz. c. Suppose you measured the cans of a random 36-pack and got a sample mean of 12.19 oz. Is it reasonable to assume that the actual population mean is 12.00 oz? Why or why not?Suppose that you have a four-sided die that is equally weighted (i.e. equal chance of any of the four sides landing face up). The four values on the die are [12.5968, 2, -2 and -12.5968] . What is the standard deviation using the conceptual definition? That is, what is the average distance from the data points to the mean? A. 5.34 B. 4.09 C. 2.58 D. 7.29
- The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 67 minutes and a standard deviation of 16 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible.b. Find the probability that a randomly selected person at the hot springs stays longer then 77 minutes. c. The park service is considering offering a discount for the 4% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes.d. Find the Inter Quartile Range (IQR) for time spent at the hot springs.Q1: (. ) minutesQ3: ( )minutesIQR:( )minutes PLEASE ANSWER ALL 3 SUBS B, C, AND DIII. SAMPLING AND SAMPLING DISTRIBUTIONS Assume that the systolic blood pressure of 30-year-old males is normally distributed, with an average of 122 mmHg and a standard deviation of 10 mmHg. а. b. Calculate the probability that the blood pressure of an individual male from this population will be between 118 and 124 mmHg.Suppose that the average number of Facebook friends users have is normally distributed with a mean of 112 and a standard deviation of about 48. Assume forty-six individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible. 1. the group of 46, find the probability that the average number of friends is more than 123. 2. Find the first quartile for the average number of Facebook friends.
