Question

6. A self-reported survey of 200 middle managers at a successful investment firm showed the average number of hours of exercise they participated in per week was 3.66 with a standard deviation of 4.93 hours. The survey was conducted in July. a. What percent of the sample exercised greater than 4.5 hours per week? b. What percent of the sample exercised between 3.5 and 4 hours per week? c. The top 5% of the managers surveyed exercised how many hours or more per week? d. Why might a company care about the amount of exercise their employees get per week?

Answer 1

A self-reported survey of 200 middle managers therefore, sample size is large enough here.

Consider, x = number of hours of exercise they participated in per week

a)

percent of the sample exercised greater than 4.5 hours per week

P[x>4.5]

=P[z>0.17]

=1-NORMSDIST(0.17)..............................by using Excel

=0.4325

Therefore, 43.25 % of the sample exercised greater than 4.5 hours per week

b) percent of the sample exercised between 3.5 and 4 hours per week

P[3.5<x<4]

=P[-0.03<z<0.07]

=NORMSDIST(0.07) - NORMSDIST(-0.03)......................by using Excel.

=0.0399

Therefore, 3.99 percent of the sample exercised between 3.5 and 4 hours per week.

c) top 5% mean 95% below

Therefore,

P[x<a] = 0.95

.....................by using NORMSINV(0.95)

=> a= 1.645*4.93 + 3.66

=> a= 11.77

Therefore, The top 5% of the managers surveyed exercised 11.75 hours or more per week.

d)

a company care about the amount of exercise their employees get per week for successful firm.