Question
A survey of 200 middle managers showed a distribution of the number of hours of exercise...
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.
Answers
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)
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