# Construction site

A cement truck delivers mixed cement to a large construction site. Let x represent the cycle time in minutes for the truck to leave the construction site, go back to the cement plant, fill up, and return to the construction site with another load of cement. From past experiences, it is known that the mean cycle time is μ = 46 minutes with σ = 9 minutes. The x distribution is approximately normal. What is the probability that the cycle time will exceed 61 minutes, given that it has exceeded 44 minutes?
A certain company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a battery is normally distributed, with a mean of 50 months and a standard deviation of 9 months. If the company does not want to make refunds for more than 10% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
A person’s level of blood glucose and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 73 and standard deviation of σ = 20. What is the probability that, for an adult after a 12-hour fast, x is more than 85?
A person’s level of blood glucose and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 90 and standard deviation of σ = 21 What is the probability that, for an adult after a 12-hour fast, x is less than 53?
A person’s level of blood glucose and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 81 and standard deviation of σ = 21. What is the probability that, for an adult after a 12-hour fast, x is between 113 and 121?

Assume that about 40% of all U.S. adults try to pad their insurance claims. Suppose that you are the director of an insurance adjustment office. Your office has just received 108 insurance claims to be processed in the next few days. What is the probability that fewer than 40 of the claims have been padded?
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Assuming that the heights of college women are normally distributed with mean 62 inches and standard deviation 3.5 inches, what percentage of women are taller than 55 inches?
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Assuming that the heights of college women are normally distributed with mean 64 inches and standard deviation 1.5 inches, what percentage of women are between 65.5 inches and 68.5 inches?
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Find the area under the standard normal curve over the interval specified below.

Find the area under the standard normal curve over the interval specified below.

Find the area under the standard normal curve over the interval specified below.

Find z such that 62.1% of the standard normal curve lies to the left of z.
Find z such that 90.1% of the standard normal curve lies between -z and z.

Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. Suppose that for healthy females, x has an approximately normal distribution with mean μ = 4.8 and standard deviation σ = 0.3 Convert the following x interval from a laboratory test to a z interval.

3.9 < x < 5.4
Question text
Let z be a random variable with a standard normal distribution. Find the indicated probability below.

P(0.5 ≤ z ≤ 1.4)

Question text
Let z be a random variable with a standard normal distribution. Find the indicated probability below.

Let z be a random variable with a standard normal distribution. Find the indicated probability below.
P(z ≥ 2)

Suppose a certain species of fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean  kilograms and standard deviation  kilograms. Let x be the weight of a fawn in kilograms. Convert the following x interval to a z interval. Round to the nearest hundredth.
The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that an 18-year-old man selected at random is greater than 74 inches tall?
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The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the average height  of a sample of twenty 18-year-old men will be less than 69 inches? Round your answer to four decimal places.
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The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the height of an 18-year-old man selected at random is between 69 inches and 73 inches?
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The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the average height  of a sample of ten 18-year-old men will be between 71 and 78 inches?