Answer to Question #195108 in Statistics and Probability for you

Question #195108

A school principal claims that grade 11 students have a mean grade of 86 with a standard deviation of 4. suppose that the distribution is approximately normal. What is the probability that a random selected grade will be greater than 82 but less that 90?


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Expert's answer
2021-05-19T16:36:11-0400

Let X=X= grade: XN(μ,σ2)X\sim N(\mu,\sigma^2)

Given μ=86,σ=4\mu=86, \sigma=4

P(82<X<90)=P(X<90)P(X82)P(82<X<90)=P(X<90)-P(X\leq82)

=P(Z<90864)P(Z82864)=P(Z<\dfrac{90-86}{4})-P(Z\leq\dfrac{82-86}{4})

=P(Z<1)P(Z1)=P(Z<1)-P(Z\leq-1)

0.841340.158660.6827\approx0.84134-0.15866\approx0.6827


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