1. Let X be a random variable with u = 79 and o = 7. The distribution is normal and the sample size is 10. Find the probability that the score selected randomly is less than 85. a.
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- Suppose that the weight of seedless watermelons is normally distributed with mean 6 kg. and standarddeviation 1.4 kg. Let X be the weight of a randomly selected seedless watermelon. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ Nb. What is the median seedless watermelon weight? c. What is the Z-score for a seedless watermelon weighing 7 kg? d. What is the probability that a randomly selected watermelon will weigh more than 5.3 kg? e. What is the probability that a randomly selected seedless watermelon will weigh between 5.2 and 5.7 kg? f. The 75th percentile for the weight of seedless watermelons is kg.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)Suppose that the speed at which cars go on the freeway is normally distributed with mean 79 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( 79 5 or or b. If one car is randomly chosen, find the probability that it is traveling more than 78 mph. Round to 4 decumal places. c. If one of the cars is randomly chosen, find the probability that it is traveling between 81 and 86 mph. Round to 4 decimal places.
- PleaseSuppose that the speed at which cars go on the freeway is normally distributed with mean 80 mph and standard deviation 10 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 79 mph. Round to 4 decumal places. c. If one of the cars is randomly chosen, find the probability that it is traveling between 83 and 86 mph. Round to 4 decimal places.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.
- 1. If Z is a standard normal variable, find the probability that Z lies between 0.25 and 1.67. Draw diagram for normal distribution, define the desired probability as shaded area, use Table to calculate this probability, and circle one of the multiple choice answers. P(0.25< Z < 1.67) =A) – 0.3538 B) 0.9525 C) 0.3538 D) 1.5512Suppose a random sample of n measurements is selected with probability of success p = . 35. Given n = 200, describe the shape, and find the mean and the standard deviation of the sampling distribution of the sample proportion.A population has a normal distribution. A sample size of n is selected from this popuiation. Descriee theshape of the sampling distribution Of the sampre mean for eaen of the foliaung cars. a.73D23 b.n=450
- The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 74 minutes and a standard deviation of 17 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. a. What is the distribution of X? X - N b. Find the probability that a randomly selected person at the hot springs stays longer then 85 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 (1QR) for time spent at the hot springs. Q1: minutes Q3: minutes IQR: minutesWe are given a normally distributed random variable X with µ = 75 and σ = 5. Find P (X > 85). 2.Find k such as P(X<k) = 0.997. Interpret your result. 3.Find the two values where the middle 68.27% of the distribution of X lie.Suppose a population with a mean of 100 and a variance of 900 was given. The central limit theorem was applied with a sample size ?? ≥ 25. A random sample of size ?? = 30 wasobtained. Find the: i. mean and variance of sampling distribution for sample means. ii. probability that 96 ≤ ??̅≤ 110. iii. probability that ??̅≤ 107.