Answer to Question #192950 in Statistics and Probability for Millicent

Question

UESTION TWO

The time it takes a randomly selected employee to perform a task is mean value of 120 seconds and standard deviation of 20 seconds.

INCOME-y 28

31

34

30 35 158

            Calculate the probability that a randomly selected employee will complete:

2.1.1 The task within 100 to 130 sec (5)

2.1.2 In more than 75sec

Answer 1

2.1.1 $P(100<X<130)=P(\frac{100-120}{20}<Z<\frac{130-120}{20})]P(-1<Z<0.5)=$

$=P(Z<0.5)-P(Z<-1)=0.6915-0.1587=0.5328.$

2.1.2 $P(X>75)=P(Z>\frac{75-120}{20})=P(Z>-2.25)=0.9878.$