Answer to Question #220365 in Statistics and Probability for bob

Question #220365

The math contest called the Fermat is out of 150 points. The mean score this year is 91 points with a standard deviation of 12. Students in the top 25% receive a medal. Assuming the scores are normally distributed, what mark is required to receive a medal? *




1
Expert's answer
2021-07-26T14:26:08-0400


Given that:

μ=91\mu=91

σ=12\sigma=12

n=150n=150


λ=?\lambda=?


Area:10.25=0.75Area: 1-0.25=0.75

The ZScoreZ-Score of 0.750.75 is 0.670.67.

Zscore=λμσnZ-score=\frac{\lambda -\mu }{\frac{\sigma }{\sqrt{n}}}

0.67=λ91121500.67=\frac{\lambda -91}{\frac{12}{\sqrt{150}}}

λ91=0.67×12150\lambda -91=0.67\times \frac{12}{\sqrt{150}}

λ=(0.67×12150)+91\lambda =\left(0.67\times \frac{12}{\sqrt{150}}\right)+91

λ=91.656591.66\lambda =91.6565\approx 91.66


Therefore, 91.6691.66 are required to receive a medal.

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