Assume the random variable x is normally distributed with mean u = 86 and standard deviation o = 5. Find the indicated probability P(x <83)

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b) 62.47% of the students are between 14 and 18 years old.

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mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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