Question

A survey of 200 middle managers showed a distribution of the number of hours of exercise they participated in per week with a mean of 3.71 hours and a standard deviation of

4.92 hours. Complete parts​ (a) through​ (c) below.

​a) According to the Normal​ model, what percent of managers will exercise fewer than one standard deviation below the mean number of​ hours?

___ ​% (Round to the nearest whole number as​ needed.)

​b) For these​ data, what does that​ mean? Explain. Select the correct choice below and fill in the answer​ box(es) within your choice.

​(Type integers or​ decimals.)

A.One standard deviation below the mean is ___ hours, which is impossible.

B.One standard deviation below the mean is ___hours. This means that ___% of managers are exercising exactly this number of hours.

C.One standard deviation below the mean is ___ hours. This means that ___% of managers are exercising no fewer than this number of hours.

D.One standard deviation below the mean is ___ hours. This means that ___% of managers are exercising no fewer than this number of hours.

​

c) Explain the problem in using the Normal model for these data. Choose the correct answer below.

A. The distribution is uniform.

B. The distribution is strongly skewed to the​ left, not symmetric.

C. The distribution is strongly skewed to the​ right, not symmetric.

D. The distribution is exponential.

Answer 1

Given that, u3.71, a 4.92 Let X denotes the managers will exercise fewer than one standard deviation below the mean number ofhours X=μ-1σ =3.71-1*4.92 -1.21 The percent of managers will exercise fewer than one standard deviation below the mean number ofhours is X-и -1.21-3.71 P(X-1.21) P 4.92 =P(Z<-1.00) (Using the z-table) = 0.1587 16% b) One standard deviation below the mean is =3.71-4.92= -1.21 hours, which is impossible. (as time cannot be negative) Answer: option (A) c) The distribution is strongly skewed to the right, not symmetric Act Go Answer: option (c)