Question #341551

The Test score for a class are normally distributed . what is the the probability a student scored above 90. Given: µ = 75

Ơ = 10

1
Expert's answer
2022-05-17T00:12:53-0400

We have a normal distribution, μ=75,σ=10,x=90.\mu=75, \sigma=10,x=90.

Let's convert it to the standard normal distribution,

z=xμσ=907510=1.5;P(X>90)=P(Z>1.5)=1P(Z<1.5)==10.9332=0.0668 (from z-table).z=\cfrac{x-\mu}{\sigma}=\cfrac{90-75}{10}=1.5; \\P(X>90)=P(Z>1.5)=1-P(Z<1.5)=\\ =1-0.9332=0.0668\text{ (from z-table)}.




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