Question

12.

In a sample of Starbucks customers it was found that the number of individual items bought per month at Starbucks was 15 with a standard deviation of 17. Assume the data to be approximately bell-shaped. Approximately 95% of the time, the number of monthly items purchased was between two values A and B. What is the value of B? Write only a number as your answer.

13.

A study studied the birth weights of 1,729 babies born in the United States. The mean weight was 3234 grams with a standard deviation of 871 grams. Assume that birth weight data are approximately bell-shaped. Estimate the number of newborns who weighed between 1492 grams and 4976 grams. Write only a number as your answer. Round your answer to the nearest whole number.

14.

For a certain type of truck, the mean number of miles per gallon is 23.5 and the standard deviation is 4.3 . Assume gas mileage for this type of truck to be approximately bell-shaped. Compute the z-score for a truck whose gas mileage is 14 .

Write only a number as your answer. Round your answer to two decimal places (for example: 3.15).

15.

A population has mean 26 and standard deviation 8 . What is the data value that has a z-score of 1 ? Write only a number as your answer.

Answer 1

(12)

By 68-95-99.7 Rule, about 95% of the values fall within two standard deviations from mean.

So,

B is given by:

So,

Answer is:

49

(13)

= 3234

= 871

To find P(1492 <X < 4976):

Case 1: For X from 1492 to mid value:

Z = (1492 - 3234)/871

= - 2.00

Table of Area Under Standard Normal Curve gives area = 0.4772

Case 2: For X from mid value to 4976:

Z = (4976 - 3234)/871

= 2.00

Table of Area Under Standard Normal Curve gives area = 0.4772

So,

P(1492 <X < 4976) = 2 X 0.4772 = 0.9544

So,

Number of newborns = 1729 X 0.9544 = 1650 (Round to integer)

So,

Answer is:

1650

(14)

= 23.5

= 4.3

X = 14

Z = (14 - 23.5)/4.3

= - 2.21

So,

Answer is:

-2.21

(15)

= 26

= 8

Z = 1

Z = 1 = (X - 26)/8

So,

X = 26 + (1 X 8)

   = 34

So,

Answer is:

34