**Question**

In a survey of men agedÂ 20-29Â in a country, the mean height wasÂ 73.4Â inches with a standard deviation ofÂ 2.7Â inches. Find the minimum height in the topÂ 10%Â of heights.

**Question**

Two thousand students took an exam. The scores on the exam have an approximate normal distribution with a mean ofÂ Î¼=81Â points and a standard deviation ofÂ Ïƒ=4Â points. The middleÂ 50%Â of the exam scores are between what two values?

**Question**

On average,Â 28Â percent ofÂ 18Â toÂ 34Â year olds check their social media profiles before getting out of bed in the morning. Suppose this percentage follows a normal distribution with a random variableÂ X, which has a standard deviation of five percent. Find the probability that the percent ofÂ 18Â toÂ 34Â year olds who check social media before getting out of bed in the morning is, at most,Â 32.

**Question**

A worn, poorly set-up machine is observed to produce components whose lengthÂ XÂ follows a normal distribution with meanÂ 14Â centimeters and varianceÂ 9. Calculate the probability that a component is at leastÂ 12Â centimeters long.

**Question**

Sugar canes have lengths,Â X, that are normally distributed with meanÂ 365.45Â centimeters and standard deviationÂ 4.9Â centimeters. What is the probability of the length of a randomly selected cane being betweenÂ 360Â andÂ 370Â centimeters?

**Question**

Suppose that the weight,Â X,Â in pounds, of aÂ 40-year-old man is a normal random variable with meanÂ 147Â and standard deviationÂ 16. CalculateÂ P(120â‰¤Xâ‰¤153).â€‹

**Question**

A tire company finds the lifespan for one brand of its tires is normally distributed with a mean ofÂ 47,500Â miles and a standard deviation ofÂ 3,000Â miles. What mileage would correspond to the the highestÂ 3%Â of the tires?

**Question**

A firmâ€™s marketing manager believes that total sales for next year will follow the normal distribution, with a mean ofÂ $3.2Â million and a standard deviation ofÂ $250,000. Determine the sales level that has only aÂ 3%Â chance of being exceeded next year.

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