Question

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1.

Which of the following best describes a z-score?

A normal distribution with a mean of 0 and a standard deviation of 1.

• The area under the density function.
• Finding a data point, given the probability of being less than that data point.
• The number of standard deviations from the mean.
• Finding the probability of being between two data points.

2.

Which of the following is the purpose of invNorm in the calculator?

• A normal distribution with a mean of 0 and a standard deviation of 1.
• Finding a data point, given the probability of being less than that data point.
• The number of standard deviations from the mean.
• Finding the probability of being between two data points.
• The area under the density function.

3.Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading greater than 1.865°C.

P(Z>1.865)=P(Z>1.865)=  (Round to four decimal places)

4.Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading greater than -2.111°C.

P(Z>−2.111)=P(Z>-2.111)=  (Round to four decimal places)

5.About ____ % of the area under the curve of the standard normal distribution is between z=−0.213z=-0.213 and z=0.213z=0.213 (or within 0.213 standard deviations of the mean).

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

6.Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between -2.154°C and -1.206°C.

P(−2.154<Z<−1.206)=P(-2.154<Z<-1.206)=  (Round to four decimal places)

7.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 60.5 with a standard deviation of 8.7. Assume that the distribution is approximately normal.

Find the probability that an elite athlete has a maximum oxygen uptake of at most 37 ml/kg.  (Round answer to four decimal places.)

8.The mean daily production of a herd of cows is assumed to be normally distributed with a mean of 39 liters, and standard deviation of 5.6 liters.

What is the probability that daily production is between 30.9 and 46.1 liters?  (Round your answer to 4 decimal places.)

9.A particular fruit's weights are normally distributed, with a mean of 788 grams and a standard deviation of 36 grams.

If you pick one fruit at random, what is the probability that it will weigh between 690 grams and 910 grams?  (Round answer to four decimal places.)

10.A manufacturer knows that their items have a normally distributed length, with a mean of 5 inches, and standard deviation of 0.7 inches.

If one item is chosen at random, what is the probability that it is less than 6.9 inches long?  (Round to four decimal places.)

11.Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.

If P(z<e)=0.0141P(z<e)=0.0141, find e.

(Round to four decimal places.)

12.For a standard normal distribution, find:

P(z>c)=0.3131P(z>c)=0.3131

c=

(Round to two decimal places.)

13.Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.

If P(−b<z<b)=0.6724P(-b<z<b)=0.6724, find b.

b=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-b to bb? (given in the problem)
• What is the area under the normal curve that is NOT between −b-b and bb? (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-b? (Use symmetry of normal distribution.)
• Given that information, what calculator function can you use to find −b-b?
• Now find b.

14.Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.

If P(0<z<a)=0.4932P(0<z<a)=0.4932, find a.

a=

(Round to two decimal places.)

Answer 1

1. The number of standard deviations from the mean.

2.The area under the density function

3. P( Z > 1.865 )= 1- P(Z < 1.865) = 1-0.96856=0.0314

4. P( Z > -2.11) = P(Z < 2.11) = 0.98257

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