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in order to qualify for a police academy, applicants are given a test of physical fitness. The scores are normally distributed with a mean of 60 and a standard deviation of 12. If only the top 20% of the applicants are selected find the cutoff score. Round value calculations to 2 decimal places and final answer to the nearest whole number

User Nugu
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2 votes

Answer:

The cutoff score is 71.

Explanation:

We are given that the scores are normally distributed with a mean of 60 and a standard deviation of 12.

If only the top 20% of the applicants are selected we have to find the cut off score.

Let X = sample mean daily precipitation

So, X ~ Normal(
\mu=60,\sigma^(2) =12^(2))

The z score probability distribution for normal distribution is given by;

Z =
( X-\mu)/(\sigma ) } ~ N(0,1)

where,
\mu = population mean score = 60


\sigma = standard deviation = 12

Now, we have to find the cut off score at which the top 20% of the applicants are selected, that is;

P(X
\geq x) = 0.20 {where x is the required cut off score}

P(
( X-\mu)/(\sigma ) }
\geq
(x-60)/(12 ) } ) = 0.20

P(Z
\geq
(x-60)/(12 ) } ) = 0.20

Now, in the z table the critical value of x that represents the top 20% of the area is given as 0.8416, i.e;


(x-60)/(12 ) } = 0.8416


{x-60}}= 0.8416 * 12

x = 60 + 10.09 = 70.09 ≈ 71

Hence, the cutoff score is 71.

User Boyd
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