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# Standard Normal Probability Distribution question

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Intern
Joined: 03 Jul 2010
Posts: 11
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Standard Normal Probability Distribution question [#permalink]

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06 Jul 2010, 12:49
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Hi,

Can someone advise me if my calculation for the below question is correct.

Q1. An HR Manager is concerned about the absenteeism of hourly employees, especially on Wednesday in the summer months. He has collected data for Wednesday in May over the past 6 years as follows:

No. absent No. absent No. absent
103 96 114
91 84 69
100 98 89
87 97 93
65 104 88
104 112 102
119 88 109
103 96 93

Find the mean number of employees absent as well as the standard deviation. If absenteeism on Wednesday in May is felt to be normally distributed, what is the probability there would be more than 112 people absent on a Wednesday in May?

My calculation:

A. Mean = 96
B. Standard Deviation = 12.41 or 12

C. Probability of more than 112 people absent on Wednesday in month of May

where:
mean = 96
std. dev. = 12
X = 112

Z score computation:

z= X - mean / std.dev

z = 112 - 96 / 12

z = 1.33 = 0.4082

On Z distribution table, the value of 1.33 is 0.4082

Since X is greater than the mean value

P(X) = 0.5 + Z = 0.5 + 0.4082 = 0.91 or 91%

Appreciate for a positive feedback.

Thanks.
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Joined: 17 Nov 2007
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Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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Re: Standard Normal Probability Distribution question [#permalink]

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06 Jul 2010, 14:42
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Expert's post
First of all it's not a GMAT question.

Your solution seems to be right except one thing: the question asks "...would be more than 112 people...". So, it's rather 100 - 91 = 9%
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Re: Standard Normal Probability Distribution question   [#permalink] 06 Jul 2010, 14:42
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