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Chapter 2: Q. 121 (page 159)

Use the following information to answer the next two exercises. X= the number of days per week that 100clients use a particular exercise facility.

The number that is 1.5standard deviations BELOW the mean is approximately

a.0.7b.4.8c.-2.8d.Cannotbedetermined

Short Answer

Expert verified

The answer is a.

The number that is 1.5standard deviation BELOW the mean is approximately 0.7.

Step by step solution

01

Given 

X= the number of days per week that 100clients use a particular exercise facility.

02

Explanation 

Xis the number of days per week that100clients use a particular exercise facility.

n=100

x¯=0(3)+1(12)+2(33)+3(28)+4(11)+5(9)+6(4)100

x¯=275100=2.75

The sample variance, s2, is equal to the sum of the last column (184.75)divided by the total number of data values minus one (100-1)

localid="1649444160964" s2=∑f(x-x¯)2n-1=184.75100-1=1.866

The square root of the sample variance equals the sample standard deviation s.

localid="1649444175515" s=1.866=1.3660

value=mean+(#ofSTDEV)(standard_deviation)

x=x¯+(#of STDEV)(s)

x=2.75-1.5(1.3660)

x=0.701

As a result, the number 1.5standard deviations below the mean is roughly 0.7.

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