Question

1. The weekly salaries of teachers in one state are normally distributed with a mean of 560.0 dollars and a standard deviation of 39.0 dollars. What is the probability that a randomly selected teacher earns more than 605.0 a week?

SELECT ALL APPLICABLE CHOICES

A)

87.57187%87.57187%

B)

14.42813%14.42813%

C)

8.428135%8.428135%

D)

4.428135%4.428135%

E)

12.42813%12.42813%

F) None of These

2.

The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 85 inches, and a standard deviation of 12 inches. What is the probability that the mean annual precipitation during 48 randomly picked years will be less than 87.4 inches?

SELECT ALL APPLICABLE CHOICES

A)

87.70717%87.70717%

B)

97.70717%97.70717%

C)

95.70717%95.70717%

D)

91.70717%91.70717%

E)

85.70717%85.70717%

F)

8.292833%8.292833%

G) None of These

Answer 1

1.
First of all, we have to calculate Z score
Z score = (605 - 560) / 39 = 1.15

As per Z table, area to the left of Z score is 0.8749

As we want probability for greater than 605, it is 1 - 0.8749 = 0.1251 or 12.51%

Answer is E) 12.42813%

2.
Mean of randomly selected 48 years = 12 / Sqrt 48 = 1.73
First of all, we have to calculate Z score
Z score = (87.4-85) / 1.73 = 1.39

As per Z table, area to the left of Z score is 0.9177

As we want probability for less than 87.4, it is 0.9177 or 91.77%

Answer is D) 91.7071%

Difference is due to error of rounding off