High School

The distribution of weights of female college cross country runners is approximately normal with a mean of 122 pounds and a standard deviation of 8 pounds.

Which of the following is closest to the percent of the runners who weigh between 114 pounds and 138 pounds?

A. 68%
B. 75%
C. 85%
D. 95%

Answer :

The percentag.e of female college runners between 114 - 138 pounds is 82%

What % of runners weigh 114 - 138 pounds?

Given that X is normally distributed with mean μ = 122 pounds and standard deviation σ = 8 pounds.

We want to find [tex]P(114 < X < 138)[/tex]

To get this, we will standardize X first:

[tex]P(114 < X < 138) = P((114 - 122)/8 < (X - 122)/8 < (138 - 122)/8)[/tex]

= P(-1 < Z < 2)

Using standard normal table, we find that probability of Z falling between -1 and 2 is:

= 0.8186

That means:

[tex]P(114 < X < 138)[/tex] = 0.8186

[tex]P(114 < X < 138)[/tex] = 81.86%

[tex]P(114 < X < 138)[/tex] = 82%

Missing options:

(A)18% (B) 32% (C) 68% (D) 82% (E)95%

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