A normal population has a mean of 80.0 and a standard deviation of 14.0. Compute

remolatg

remolatg

Answered question

2021-10-13

A normal population has a mean of 80.0 and a standard deviation of 14.0. Compute the probability of a value between 75.0 and 90.0.

Answer & Explanation

Ayesha Gomez

Ayesha Gomez

Skilled2021-10-14Added 104 answers

Mean of the normal distribution is μ=80 and the standard deviation is σ=14
Let X serve as the random element.
P(75<X<90)=P(75μ<Xμ<90μ)
=P(75μσ<Xμσ<90μσ)
=P(758014<z<908014)
=P(514<z<1014)
=P(-0.357) Calculate because the two points are on opposite sides of the mean.
P(-0.357 P(75 =P(0 =0.1406+0.2611 (from Appendix B1.)
=0.4017

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