1-

About __________% of the area under the curve of the standard normal distribution is between z=0.716 and z=0.716 (or within 0.716 standard deviations of the mean).

(Notice that the percent sign is already there. You should round to two decimal places.)

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2-

The physical fitness of an athlete is often measured by how much oxygen the athlete takes in (which is recorded in milliliters per kilogram, ml/kg). The mean maximum oxygen uptake for elite athletes has been found to be 61 with a standard deviation of 7.6. Assume that the distribution is approximately normal. Find the probability that an elite athlete has a maximum oxygen uptake of at most 52.6 ml/kg. _______________(Round answer to four decimal places.)

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3-

A particular fruit's weights are normally distributed, with a mean of 551 grams and a standard deviation of 10 grams. If you pick one fruit at random, what is the probability that it will weigh between 553 grams and 558 grams? _______(Round answer to four decimal places.)

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4-

In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 53.1 inches, and standard deviation of 4.1 inches. What is the probability that a randomly chosen child has a height of more than 40.9 inches? (Round your answer to 4 decimal places.)

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5-

For a standard normal distribution, given: P(z

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6-

Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(z>c)=0.0507 c=______ (Round to two decimal places.)

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7-

Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(bb. b= (Round to two decimal places.)

Hint: Consider symmetry on this problem and draw a picture of the normal distribution to visualize this problem.

• What is the area under the normal curve from b to b? (given in the problem)
• What is the area under the normal curve that is NOT between b and b? (Complement of the answer to the first part of the hint)
• Given that information, what is the area under the normal curve from to b? (Use symmetry of normal distribution.)
• Given that information, what calculator function can you use to find b?
• Now find b.

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8-

Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(0a. a=_____ (Round to two decimal places.)

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9-

The lengths of pregnancies in a small rural village are normally distributed with a mean of 260 days and a standard deviation of 17 days. A distribution of values is normal with a mean of 260 and a standard deviation of 17. What percentage of pregnancies last fewer than 277 days? P(X < 277 days) = % Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign).

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10-

Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with a mean of 57.9 ft and a standard deviation of 4.8 ft. A tree of this type grows in my backyard, and it stands 42.5 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter. P(X<42.5)=____ Enter your answer accurate to 4 decimal places.

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11-

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 222.8-cm and a standard deviation of 1.8-cm. Find the probability that the length of a randomly selected steel rod is less than 226.4-cm. P(X < 226.4-cm) = Enter your answer as a number accurate to 4 decimal places.

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12-

In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 56.7 inches, and standard deviation of 9.3 inches. What is the probability that the height of a randomly chosen child is between 50.75 and 75.25 inches? (Round your answer to 4 decimal places.)

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13-

Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 12.8 years and a standard deviation of 2.2 years. Find the probability that a randomly selected quartz time piece will have a replacement time less than 6.4 years? P(X < 6.4 years) = Enter your answer accurate to 4 decimal places. If the company wants to provide a warranty so that only 1.1% of the quartz time pieces will be replaced before the warranty expires, what is the time length of the warranty? warranty = years Enter your answer as a number accurate to 1 decimal place.

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14-

An electronic product takes an average of 5 hours to move through an assembly line. If the standard deviation of 0.7 hours, what is the probability that an item will take between 3.2 and 6.9 hours to move through the assembly line? (Round your answer to 4 decimal places.)

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15-

A distribution of values is normal with a mean of 247 and a standard deviation of 9. Find the probability that a randomly selected value is between 234.4 and 270.4. P(234.4

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16-

Let X represent the full height of certain species of tree. Assume that X is normally distributed with a mean of 157.3 feet and a standard deviation of 52.6 feet. Find the probability that the full height of a randomly selected tree is greater than 136.3 feet. P(X>136.3)= Enter your answer as a number accurate to 4 decimal places.

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17-

The heights of adult men in America are normally distributed, with a mean of 69.6 inches and a standard deviation of 2.68 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.1 inches and a standard deviation of 2.54 inches. If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)? z= If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)? z= Who is relatively taller?

• The 6 foot 3 inch American man
• The 5 foot 11 inch American woman