Question

QUESTION 1: An analysis of a performance of the employees in a month follows normal distribution. The mean of the distribution is 95 and the standard deviation is 9. The team leader decided to award an A category to the employees whose performance are in the highest 20 percent. What is the dividing point for those employees who earn an A and those earning a B?

QUESTION 2: A survey revealed that 85 percent of women do bargaining while shopping. Use the continuity correction factor if needed.
a. During a period in which 300 women visited a store what is the probability that more than 242 of them bargained?
b. During a period in which 300 women visited a store what is the probability that less than 250 of them bargained?

Answer 1

Question 1)

Answer)

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

From z table, p(z>0.84) = 0.2

And we know that z = (x-mean)/s.d

0.84 = (x-95)/9

X = 102.56

Question 2)

Answer)

Given n = 300

P = 0.85

Mean is given by n*p = 255

S.d is given by √{n*p*(1-p)} = 6.18465843842

1)

P(x>242)

Z = (x-mean)/s.d

By continuity correction

We will find p(x>242.5)

Z = -2.02

From z table, p(z>-2.02) = 0.9783

2)

P(x<250)

By continuity correction

P(x<249.5)

Z = -0.89

From z table, p(z<-0.89) = 0.1867