Answer to Question #328223 in Statistics and Probability for Coe

Question

The average time it takes a group of Senior High School students to complete a certain examination is 48.2 minutes. The standard deviation is 7 minutes. If 45 randomly selected college student take the examination, what is the probability that the mean time it takes the group to complete the test between 46 and 49 minutes?

Answer 1

We have a normal distribution, $μ=48.2,σ=7,n=45.$

Let's convert it to the standard normal distribution,

$\bar{z}=\cfrac{\bar{x}-\mu}{\sigma/\sqrt{n}},\\ \bar{z}_1=\cfrac{46-48.2}{7/\sqrt{45}}=-2.11,\\ \bar{z}_2=\cfrac{49-48.2}{7/\sqrt{45}}=0.77,\\ P(46<\bar{X}<49)=P(-2.11<\bar{Z}<0.77)=\\ =P(\bar{Z}<0.77)-P(\bar{Z}<-2.11)=\\ =0.7794-0.0174=0.7620\text{ (from z-table).}$

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