Let X = number of miles a family travels for summer vacation. X follows a normal distribution with a mean of 311 miles and standard deviation of 162 miles. Calculate the probability that a family traveled between 210 and 520 miles.

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Let X = number of miles a family travels for summer vacation. X follows a normal distribution with a mean of 311 miles and standard deviation of 162 miles. Calculate the probability that a family traveled between 210 and 520 miles. 

Expert Solution
Step 1: Introduce the given information

From the given information,

X follows a normal distribution with a mean of 311 miles and standard deviation of 162 miles

ie,

 Mean = mu space equalsstandard deviation equals sigma space equals162

standard deviation equals sigma space equals162

Using formula ,

Z space equals space fraction numerator X minus mu over denominator sigma end fraction

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