Question

1. Jason is thinking about getting a trampoline for his son's birthday party. He knows that the weights of children are normally distributed, with a mean of 70 pounds and a standard deviation of 8 pounds. a) Jason decides to set the limit to 4 children on the trampoline. What does Central Limit Theorem (CLT) tell us about the mean and standard error of the sampling distribution of means for random samples of size 4 children? b) Sketch the sampling distribution of means for average weights for samples of size 4 children below. c) The trampoline has a 300 paund weight capacity. Calculate the probability that a random sample of 4 children would have a mean weight over the maximum average. Make sure to label and shade the Standard Normal Distribution appropriately. d) Do you think this is a safe limit? Why or why not?

Answer 1

solution :- M = 70 o=8 D el = lix 70 a TE 41 SE colle 4 X a Normal b 58 62 66 70 74 78 82 300 75 weight limit 4. 7 Plx>75) = 1/2, 75-70) 4 - 1.25 Plzs 23 1.25) 0.1056 t 2 -) limit is d) sime, Average weigh Exceeds weight not unusual So, This is not safe