Question

3. A distinguishing characteristic of entrepreneurs is their willingness to take risks. R.H.Brockhaus (Academy of Management Journal, Sept. 1980) used a choice dilemma questionaire (CDQ) to measure the risk-taking propensities of successful entrepreneurs (lower scores associated with a higher tendency for risk taking). The CDQ scores are normally distributed with a mean of 72 and a standard deviation of 8.

(a) What is the probability that a randomly selected entrepreneur will score between 68 and 74 on the CDQ? Final answer in 4 decimals.

(b) What CDQ score differentiates the 30.5% entrepreneurs most willing to take risks from the rest

(c) Suppose a random sample of 5 entrepreneurs are selected, what is the likelihood that the average CDQ score of these 5 entrepreneurs is between 70 and 72? Use the standard normal table and express your final answer in 4 decimals.

Answer 1

P ( 68 < X < 74 )

Standardizing the value

Z = ( 68 - 72 ) / 8

Z = -0.5

Z = ( 74 - 72 ) / 8

Z = 0.25

P ( -0.5 < Z < 0.25 )

P ( 68 < X < 74 ) = P ( Z < 0.25 ) - P ( Z < -0.5 )

P ( 68 < X < 74 ) = 0.5987 - 0.3085

P ( 68 < X < 74 ) = 0.2902

Part b) What CDQ score differentiates the 30.5% entrepreneurs most willing to take risks from the rest

P ( Z < ? ) = 30.5% = 0.305

Looking for the probability of 0.305 in the standard normal table to find the critical value Z

Z = - 0.51

-0.51 = ( X - 72 ) / 8

X = ( -0.51 * 8 ) + 72

X = 67.920

Part c)  what is the likelihood that the average CDQ score of these 5 entrepreneurs is between 70 and 72

P ( 70 < X < 72 )

Standardizing the value

Z = -0.56

Z = 0

P ( -0.56 < Z < 0 )

P ( 70 < X < 72 ) = P ( Z < 0 ) - P ( Z < -0.56 )

P ( 70 < X < 72 ) = 0.5 - 0.2881

P ( 70 < X < 72 ) = 0.2119