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# 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

source..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

PÂ (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 thatÂ X<10Â is equal to the blue area under the curve.

Step 2:

SinceÂ Î¼=14Â andÂ Ïƒ=3Â we have:

PÂ (Â X<10Â )=PÂ (Â Xâ€’Î¼<10â€’14Â )=PÂ (Xâ€’Î¼Ïƒ<10â€’143)

SinceÂ xâ€’Î¼Ïƒ=ZÂ andÂ 10â€’143=â€’1.33Â we have:

PÂ (X<10)=PÂ (Z<â€’1.33)

Step 3:Â Use theÂ standard normal tableÂ to conclude that:

PÂ (Z<â€’1.33)=0.0918

2 Result

PÂ (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 thatÂ X>21Â is equal to the blue area under the curve.

Step 2:...

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

PÂ (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 thatÂ X<10Â is equal to the blue area under the curve.

Step 2:

SinceÂ Î¼=14Â andÂ Ïƒ=3Â we have:

PÂ (Â X<10Â )=PÂ (Â Xâ€’Î¼<10â€’14Â )=PÂ (Xâ€’Î¼Ïƒ<10â€’143)

SinceÂ xâ€’Î¼Ïƒ=ZÂ andÂ 10â€’143=â€’1.33Â we have:

PÂ (X<10)=PÂ (Z<â€’1.33)

Step 3:Â Use theÂ standard normal tableÂ to conclude that:

PÂ (Z<â€’1.33)=0.0918

2 Result

PÂ (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 thatÂ X>21Â is equal to the blue area under the curve.

Step 2:...

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