Question 1: A normal population has mean = 36 and standard deviation = 8. (a) What proportion
Question:
Question 1:
A normal population has mean = 36 and standard deviation = 8.
(a) What proportion of the population is between 19 and 28?
(b) What is the probability that a randomly chosen value will be between 31 and 42?
Round the answers to at least four decimal places.
Question 2:
A normal population has mean =56 and standard deviation =7. What is the 86th percentile of the population? Use the TI-84 Plus calculator. Round the answer to at least one decimal place.
The 86th percentile of the population is blank.
Question 3:
Baby weights: The weight of male babies less than 2 months old in the United States is normally distributed with mean 11.6pounds and standard deviation 2.8pounds . Use the TI-83 Plus/TI-84 Plus calculator to answer the following. Round the answers to four decimal places.
(a) What proportion of babies weigh more than 13 pounds?
Question 4:
Baby weights: The weight of male babies less than 2 months old in the United States is normally distributed with mean 12.3 pounds and standard deviation 3.8 pounds.
(a) Find the 84th percentile of the baby weights.
(b) Find the 11th percentile of the baby weights.
(c) Find the third quartile of the baby weights.
Use the TI-84 Plus calculator and round the answers to at least two decimal places.
Question 5:
Electricity bills: According to a government energy agency, the mean monthly household electricity bill in the United States in 2011 was $109.88. Assume the amounts are normally distributed with standard deviation $23.00. Use the TI-84 Plus calculator to answer the following.
(a) What proportion of bills are greater than $129?
(b) What proportion of bills are between $86 and $140?
(c) What is the probability that a randomly selected household had a monthly bill less than $120?
Round the answers to at least four decimal places.
Question 6:
Electricity bills: According to a government energy agency, the mean monthly household electricity bill in the United States in 2011 was $109.72. Assume the amounts are normally distributed with standard deviation $17.00. Use the TI-84 Plus calculator to answer the following.
(a) Find the 7th percentile of the bill amounts.
(b) Find the 64th percentile of the bill amounts.
(c) Find the median of the bill amounts.
Round the answers to at least two decimal places.
Question 7:
How much do you study? A survey among freshmen at a certain university revealed that the number of hours spent studying the week before final exams was normally distributed with mean 26 and standard deviation 4. Use the TI-84 PLUS calculator to answer the following. Round the answer to at least four decimal places.
(a) What proportion of students studied more than 38 hours?
(b) What is the probability that a randomly selected student spent between 18 and 32 hours studying?
(c) What proportion of students studied less than 32 hours?
Question 8:
Using the TI-84 Plus calculator, find the area under the standard normal curve that lies between the following z-values. Round the answers to at least four decimal places.
(a) Find the area under the standard normal curve that lies between z=2.49 and z=0.61.
| The area between z=2.49 and z=0.61 is blank. |
Question 9:
Use the TI-84 Plus calculator to find the z-scores that bound the middle 84% of the area under the standard normal curve. Enter the answers in ascending order and round to two decimal places.
| The z-scores for the given area are blank and blank. |
Question 10:
Tree heights: Cherry trees in a certain orchard have heights that are normally distributed with mean =115 inches and standard deviation =16 inches. Use the TI-84 PLUS calculator to answer the following. Round the answers to at least two decimals.
(a) Find the 28th percentile of the tree heights.
(b) Find the 86th percentile of the tree heights.
(c) Find the first quartile of the tree heights.
(d) An agricultural scientist wants to study the tallest 1% of the trees to determine whether they have a certain gene that allows them to grow taller. To do this, she needs to study all the trees above a certain height. What height is this?
Question 11:
Flawed parts: On a certain day, a foundry manufactured 596 cast aluminum parts. Some of these had major flaws, some had minor flaws, and some had both major and minor flaws. The following table represents the results.
| Minor Flaw | No Minor Flaw | |
| Major Flaw | 17 | 33 |
| No Major Flaw | 71 | 475 |
(a) Find the probability that a randomly chosen part has a major flaw. (b) Find the probability that a randomly chosen part has a minor flaw. (c) Find the probability that a randomly chosen part has a flaw (major or minor). (d) Find the probability that a randomly chosen part has no major flaw.
Question 12:
Flu season: Suppose the following tables present the number of specimens that tested positive for Type A and Type B influenza in a country during a flu season.
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(a) Find the mean and median number of Type A cases. Round the answers to at least one decimal place. (b) Find the mean and median number of Type B cases. Round the answers to at least one decimal place. (c) A public health official says that there are more than twice as many cases of Type A influenza than Type B. Do these data support this claim?
Expert Answer:
