Question

The credit card balance for college students has a normal distribution with a mean of $3450 and a standard deviation of $995. A random sample of 37 students is selected.

1）Describe the sampling distribution of the sample mean for the 37 students

A. X ~ AN(3450,995)

B. X ~ N(3450,163.577)

C. X ~ AN(3450,163.577)

D. X ~ N(3450,995)

2）Find the probability that the mean credit card balance for the sample of 37 students is more than $3100.

A. 0.6368

B. 0.0162

C. 0.9838

D. None of these

3）Find the probability the total credit card balance for the sample of 37 students is less than $135,000.

A. 0.5793

B. 0.8869

C. 1

D. None of these

Answer 1

Solution :

A)

X N (3450 , 163.577)

option B. is correct

B)

P(x 3100) = 1 - P(x   3100)

= 1 - P[(x - ) / (3100 - 3450) / 163.577]

= 1 -  P(z 0.0162)   

= 1 - 0.0162

= 0.9838

Probability = 0.9838

option c. is correct

C)

P( < 135000) = P(( - ) / < (135000 - 3450) / 163.577)

= P(z < 804.20)

= 1

Probability = 1

option c. is correct