Question

The mean commute time for all commuting students of a university is 23 minutes with a population standard deviation of 4 minutes. A random sample of 63 driving times of commuters is taken. ̅ a) [2pts] Is the sampling distribution of the sample mean ? normal? Circle the number of i. ii. iii. iv. b) the best answer. Yes, because the sample size n is greater than 30. No, because the parent population of the data is not said to be normal. Yes, because the population standard deviation is known. No, because the sample size n is less than 30. [3pt] Find  x and  x , and sketch the sampling distribution of the sample means x . (round to 2 dec. places) _______________________________ [3pt] Find the probability the sample mean commute time is greater than 22.125 minutes. Write the statement in probability notation and give the numerical answer. Circle your final answer.

Answer 1

Ans:

sample size,n=63

Correct option is:

Yes, because the sample size n is greater than 30.

sampling distribution of the sample means(x-bar) :

mean=23

standard deviation=4/sqrt(63)=0.50

z=(22.125-23)/0.504

z=-1.736

P(z>1.736)=0.9587