Question

Full-time Ph.D. students receive an average of $12,837 per year. If the average salaries are normally distributed with a standard deviation of $1500, find these probabilities. Round the final answers to four decimal places and intermediate-value calculations to 2 decimal places. Chec Source: U.S. Education Department, Chronicle of Higher Education. Guic Part 1 Shc The student makes more than $13,900 Ask P(X> 13,900)= 0.2389 Lin Part 2 out of 2 The student makes between $13,600 and $14,600. P (13,600 s X 14,600)-| NEXT CHECK

Answer 1

1)

Answer)

As the data is normally distributed we can use standard normal z table to estimate the answers

Z = (x-mean)/s.d

Given mean = 12837

S.d = 1500

P(13600<x<14600) = p(x<14600) - p(x<13600)

P(x<14600)

Z = (14600 - 12837)/1500 = 1.18

From z table, P(z<1.18) = 0.881

P(x<13600)

Z = (13600 - 12837)/1500 = 0.51

From z table, P(z<0.51) = 0.695

Required probability is 0.881 - 0.695 = 0.186

2)

Mean = 982

S.d = 180

P(x>1290)

Z = (1290 - 982) /180 = 1.71

From z table, P(z>1.71) = 0.0436

3)

Mean = 74

S.d = 3

P(x>72)

Z = (72-74)/3 = -0.67

From z table, p(z>-0.67) = 0.7486