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1 page/≈275 words
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Level:
APA
Subject:
Mathematics & Economics
Type:
Math Problem
Language:
English (U.S.)
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Topic:

Frequency Distributions (Math Problem Sample)

Instructions:

                                           Please answer the below questions

 

The number of vacation days taken by employees of a company is normally distributed with a mean of 14 days and a standard deviation of 3 days. For the next employee, what is the probability that the number of days of vacation taken is less than 10 days? More than 21 days? Post your solutions to the problems

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Content:
Please answer the below questions
The number of vacation days taken by employees of a company is normally distributed with a mean of 14 days and a standard deviation of 3 days. For the next employee, what is the probability that the number of days of vacation taken is less than 10 days? More than 21 days? Post your solutions to the problems.
1 Result
P (X<10)=0.0918
The probability that the next employee will take a vacation of less than ten (10) days is 0.0918.
Explanation
Step 1: Sketch the curve.
The probability that X<10 is equal to the blue area under the curve.
Step 2:
Since μ=14 and σ=3 we have:
P ( X<10 )=P ( X‒μ<10‒14 )=P (X‒μσ<10‒143)
Since x‒μσ=Z and 10‒143=‒1.33 we have:
P (X<10)=P (Z<‒1.33)
Step 3: Use the standard normal table to conclude that:
P (Z<‒1.33)=0.0918
2 Result
P (X>21)=0.0099
The probability that the next employee will take a vacation of more than 21 days is very small at 0.0099.
Explanation
Step 1: Sketch the curve.
The probability that X>21 is equal to the blue area under the curve.
Step 2:...
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