Question

The amount of time a bank teller spends with each customer has a population​ mean,

muμ​,

of

2.902.90

minutes and a standard​ deviation,

sigmaσ​,

of

0.500.50

minute. Complete parts​ (a) through​ (d).

a. If you select a random sample of

1616

​customers, what is the probability that the mean time spent per customer is at least

2.8

​minutes?

. 7881.7881

​(Round to four decimal places as​ needed.)b. If you select a random sample of

1616

​customers, there is an

84​%

chance that the sample mean is less than how many​ minutes?

3.0238

​(Round to four decimal places as​ needed.)

c. What assumption must you make in order to solve​ (a) and​ (b)?

A.

That the population is uniformly distributed

B.

That the sample is symmetrically distributed and such that the Central Limit Theorem will likely hold

C.

That the population is symmetrically distributed and such that the Central Limit Theorem will likely hold for samples of size 1616

This is the correct answer.

D.

That the population is normally distributed

Your answer is not correct.d. If you select a random sample of

100

​customers, there is an

84​%

chance that the sample mean is less than how many​ minutes?

2.94952.9495

​(Round to four decimal places as​ needed.)

Answer 1

Part a)

P ( X > 2.8 ) = 1 - P ( X < 2.8 )

Standardizing the value

Z = -0.8

P ( Z > -0.8 )

P ( X > 2.8 ) = 1 - P ( Z < -0.8 )

P ( X > 2.8 ) = 1 - 0.2119

P ( X > 2.8 ) = 0.7881

Part b)

P ( Z < ? ) = 84% = 0.84

Looking for the probability 0.84 in standard normal table to find the critical value Z = 0.99

Part c)

D.

That the population is normally distributed

Part d)

P ( Z < ? ) = 84% = 0.84

Looking for the probability 0.84 in standard normal table to find the critical value Z = 0.99