In: Statistics and Probability
Having used people-counting devices at the entry to shopping centre, it is known that the average number of shoppers visiting this centre during any one-hour period is 448 shoppers, with a standard deviation of 21 shoppers. What is the probability that a random sample of 49 different one-hour shopping periods will yield a sample mean between 441 and 446 shoppers?
please type it do not handwritten
Solution :
Given that ,
mean = = 448
standard deviation = = 21
n = 49
= 448
= / n= 21 / 49=3
P(441< <446 ) = P[(441-448) /3 < ( - ) / < (446-448) / 3)]
= P(-2.33 < Z <-0.67 )
= P(Z < -0.67) - P(Z <-2.33 )
Using z table
=0.2514-0.0099
=0.2415
probability=0.2415