Which of the following normal distributions has the widest spread?

1. (2 points) Which of the following are true about all normal distributions? Check all that apply

• A. They have one large tail. • B. They are bimodal. • C. They have no major outliers. • D. They are categorically sharp.

The z-score corresponding to an observed value of a variable tells you the number of standard deviations that the observation is from the mean

• A. True • B. False

A positive z-score indicates that the observation is • A. above the mean • B. below the mean

Answer(s) submitted: • • •

(incorrect)

2. (2 points) a) Fact: the region under the standard normal curve that lies to the left of −1.95 has area 0.0255881.

Without consulting a table or a calculator giving areas under the standard normal curve, determine the area under the stan- dard normal curve that lies to the right of 1.95. answer:

b) Which property of the standard normal curve allowed you to answer part a)?

• A. The total area under the curve is 1 • B. Almost all the area under the standard normal curve

lies between −3 and 3 • C. The standard normal curve is symmetric about 0 • D. The standard normal curve extends indefinitely in

both directions • E. None of the above

Answer(s) submitted: • •

(incorrect)

3. (2 points) What are the parameters for a normal curve? • A. the sample mean and sample standard deviation • B. the population mean and population variance • C. the population mean and population standard devia-

tion • D. the population median and population standard de-

viation • E. None of the above

Answer(s) submitted:

•

(incorrect)

4. (2 points) Which of the following normal distributions has the widest spread?

• A. A normal distribution with mean 0 and standard de- viation 2

• B. A normal distribution with mean 2 and standard de- viation 1

• C. A normal distribution with mean 1 and standard de- viation 3

• D. A normal distribution with mean 3 and standard de- viation 2

• E. None of the above Answer(s) submitted:

•

(incorrect)

5. (2 points) Consider two normal distributions, one with mean −19 and standard deviation 11, the other with mean 6 and standard deviation 11. Answer the following statements using true or false.

a) The two distributions have the same shape. answer:

b) The two distributions are centered at the same place. answer:

Answer(s) submitted:

• •

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6. (2 points) The U.S. Bureau of the Census conducts nation- wide sureys on characteristics of U.S. households.

Household size Relative Frequency 1 0.1 2 0.05 3 0.275 4 0.25 5 0.125 6 0.175 7 0.025

Total 1

a) Use the previous relative frequency distribution to obtain the percentage of U.S. households that are between sizes 3 and 5. answer:

b) Use your answer from part a) to estimate the area under the corresponding normal curve that lies between 3 and 5. answer:

Answer(s) submitted: • •

(incorrect)

7. (2 points) Length of skateboards in a skateshop are nor- mally distributed with a mean of 32 in and a standard deviation of 0.6 in. The figure below shows the distribution of the length of skateboards in a skateshop. Calculate the shaded area under the curve. Express your answer in decimal form with at least two decimal place accuracy. Answer:

Answer(s) submitted: •

(incorrect)

8. (2 points) Find the following probabilities for the standard normal random variable z:

(a) P(−1.83 ≤ z ≤ 0.78) =

(b) P(−0.8 ≤ z ≤ 0.37) =

(c) P(z ≤ 0.71) =

(d) P(z >−1.16) = Answer(s) submitted:

• • • •

(incorrect)

10. (2 points) Select True or False from each pull-down menu, depending on whether the corresponding statement is true or false.

? 1. Using the standard normal curve, the z−score repre- senting the 10th percentile is 1.28.

? 2. A random variable X is normally distributed with a mean of 150 and a variance of 36. Given that X = 120, its corresponding z− score is 5.0

? 3. The mean and standard deviation of an exponential ran- dom variable are equal to each other.

? 4. The mean and standard deviation of a normally dis- tributed random variable which has been standardized are one and zero, respectively.

Answer(s) submitted:

• • • •

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11. (2 points) Suppose that X is normally distributed with mean 95 and standard deviation 28.

A. What is the probability that X is greater than 147.08? Probability =

B. What value of X does only the top 15% exceed? X =

Answer(s) submitted:

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13. (2 points) Suppose a car manufacturer believes its wind- screen wipers will last on average for three years on their cars if driven by a typical driver in the province. Moreover, the manu- facturer believes the lifetime of the wipers under such conditions is Normally distributed with a standard deviation of two years. Find the probability that, if on a car driven by a typical driver, a windscreen wiper lasts for a time that is not within 1.5 years of the mean lifetime.

The probability is: Answer(s) submitted:

• (incorrect)

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14. (2 points) An exam consists of 42 multiple-choice ques- tions. Each question has a choice of five answers, only one of which is correct. For each correct answer, a candidate gets 1 mark, and no penalty is applied for getting an incorrect answer. A particular candidate answers each question purely by guess- work.

Using Normal approximation to Binomial distribution with continuity correction, what is the estimated probability this stu- dent obtains a score greater than or equal to 10? Please use R to obtain probabilities and keep at least 6 decimal places in intermediate steps.

• A. 0.4059 • B. 0.2089 • C. 0.6643 • D. 0.5650 • E. 0.3357

Answer(s) submitted: •

(incorrect)

15. (2 points) The shelf life of a battery produced by one ma- jor company is known to be Normally distributed, with a mean life of 4 years and a standard deviation of 0.6 years.

What value of shelf life do 16% of the battery shelf lives fall above? Round your answer to one decimal place.

Answer: years. Answer(s) submitted:

• (incorrect)

16. (2 points) Cans of regular Coke are labeled as containing 12 oz. Statistics students weighed the contents of 10 randomly chosen cans, and found the mean weight to be 12.11 ounces.

Assume that cans of Coke are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard

deviation of 0.11 oz. Find the probability that a sample of 10 cans will have a mean amount of at least 12.11 oz.

Answer(s) submitted:

•

(incorrect)

17. (2 points) Assume that the readings on the thermometers are normally idstributed with a mean of 0◦ and a standard devi- ation of 1.00◦C.

Find P60, the 60th percentile.

This is the temperature reading separating the bottom 60 % from the top 40 %.

Answer(s) submitted:

•

(incorrect)

18. (2 points) Healty people have body temperatures that are normally distributed with a mean of 98.20◦F and a standard deviation of 0.62◦F .

(a) If a healthy person is randomly selected, what is the probability that he or she has a temperature above 99.6◦F?

answer:

(b) A hospital wants to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only 1 % of healty people to exceed it?

answer: Answer(s) submitted:

• •

(incorrect)

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