# Using the standard normal distribution tables, what is the area under

• Question 1
Using the standard normal distribution tables, what is the area under the standard normal curve corresponding to Z < 1.15?

• Question 2
Using the standard normal distribution tables, the area under the standard normal curve corresponding to Z > –2.62 is

• Question 3
A sample was taken of the verbal SAT scores of applicants to a California State College. The following is the five-number summary of the scores: 300, 390, 470, 600, 750. The interquartile range of these scores is

• Question 4
In a statistics class with 136 students, the professor records how much money each student has in his or her possession during the first class of the semester. The following is the data collected.
Amount No. of Students
0-9 61
10-19 44
20-29 20
30-39 5
40-49 2
50-59 3
90-99 1
The histogram for this data is

• Question 5
A sample of 20 employees from the local Honda plant was obtained and the length of time (in months) worked was recorded for each employee. A stemplot of these data follows. In the stemplot the first number in each row is the stem and the remaining numbers in the row are the leaves.
5 2 4 8 9 9
6 0 3 5 6 7 7 8 9
7 3 4 7 8 9 9
8
9 8
The median length of time worked by these 20 employees is

• Question 6
A sample was taken of the verbal SAT scores of applicants to a California State College. The following is the five-number summary of the scores: 300, 390, 470, 600, 750. About 75% of these students scored above

• Question 7
A reporter wishes to portray baseball players as overpaid. Which measure of center should he report as the average salary of major league players?

• Question 8
When water flows across farm land, some of the soil is washed away, resulting in erosion. An experiment was conducted to investigate the effect of the rate of water flow on the amount of soil washed away. Flow is measured in liters per second, and the eroded soil is measured in kilograms. The data are given in the following table.

Flow rate .31 .85 1.26 2.47 3.75

Eroded soil .82 1.95 2.18 3.01 6.07

The association between flow rate and amount of eroded soil is

• Question 9
An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used y ( in cubic feet) to heat the home and outside temperature x ( in degree-days, where a day’s degree-days are the number of degrees its average temperature falls below 65 degrees Farenheit) over a 25 month period. He then computed the least squares regression line for predicting y from x and found it to be y = 85 +16x. How much, on average, does gas used increase for each additional degree-day?

• Question 10
An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used ( in cubic feet) to heat the home and the outside temperature ( in degree-days, where a day’s degree-days are the number of degrees its average temperature falls below 65 degrees Farenheit) over a 25 month period. He then computed the least squares regression line for predicting the amount of natural gas needed to heat his home based on the outside temperature. The response variable in this model is

• Question 11
Because elderly people may have difficulty standing to have their heights measured, a study looked at predicting overall height from height to the knee. Here are data (in centimeters) for six elderly men.
Knee height x 57.7 47.4 43.5 44.8 55.2 54.6
Height y 192.3 153.3 146.4 162.7 169.1 177.8
The least squares regression line for predicting overall height from knee height is y = 42.9 + 2.5x. What is the residual for the observed knee height of 47.4?

• Question 12
Using the standard normal distribution tables, the area under the standard normal curve corresponding to –0.5 < Z < 1.2 is

• Question 13
The Insurance Institute for Highway Safety publishes data on the total damage caused by compact automobiles in a series of controlled, low-speed collisions. The following costs are for a sample of 9 cars, in hundreds of dollars.
10 6 8 10 4 3.5 7.5 8 9

What is the mean and standard deviation of the total damage caused by the cars in this sample?

• Question 14
Birthweights at a local hospital have a normal distribution with a mean of 110 oz. and a standard deviation of 15 oz. The proportion of infants with birthweights above 125 oz. is

• Question 15
The points on a scatterplot lie very close to the line whose equation is y = 4-3x. The correlation coefficient of this line is

• Question 16
Does mandatory gun ownership prevent crime? To study this, the number of burglaries committed each month in a small town were recorded for 75 months prior to passage of a bill requiring citizens to own guns and for 56 months after passage of the bill. The goal was to see if the number of burglaries committed was affected by requiring citizens to own guns. The response variable here is

• Question 17
An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used y ( in cubic feet) to heat the home and outside temperature x ( in degree-days, where a day’s degree-days are the number of degrees its average temperature falls below 65 degrees Farenheit) over a 25 month period. He then computed the least squares regression line for predicting y from x and found it to be y = 85 +16x. What is the predicted amount of gas used when the outside temperature is 10 degree-days? • Question 18
The battery in an IPod has a run-time (time until it needs to be recharged) that is normally distributed with a mean of 6 hours and a standard deviation of 30 minutes. The third quartile for this run time distribution is

• Question 19
A university professor compiles a list of all her students from the past semester. She wishes to select a sample of 3 females and 3 males. She separates female student names from the male student names and assigns a unique number , 1-56, to each female and uses a random number generator to select 3 of these numbers; then she assigns a unique number from 1-24 to each male and uses a random number generator to select three of these. The six students corresponding to the numbers selected are surveyed about their satisfaction with the textbook. This is an example of Question 20
Suppose the time that it takes a certain large bank to approve a home loan is normally distributed with mean (in days) m and standard deviation s = 1. The bank advertises that it approve loans in 5 days, on average, but measurements on a random sample of 100 loan applications to this bank gave a mean approval time of 5.2 days. Is this evidence that the mean time to approval is actually more than advertised? To answer this, we test the following hypotheses at the a=0.05 level: H0: m = 5, Ha: m> 5. What is the test statistic?

Question 21
The mean area
m of the several thousand apartments in a new development by a certain builder is advertised to be 1250 square feet. A tenant group thinks the area is less, because it is based on the square footage of apartments in an older and larger development by the same builder. The group hires an engineer to measure a sample of apartments to verify its suspicion. The appropriate null and alternative hypotheses, H0 and Ha, for m are

Question 22
I flip a coin twice and count the number of heads. What is a valid assignment of probabilities for the number of heads observed in two flips?

Question 23
Suppose the time that it takes a certain large bank to approve a home loan is normally distributed with mean (in days) m and standard deviation s = 1. The bank advertises that it approve loans in 5 days, on average, but measurements on a random sample of 225 loan applications to this bank gave a mean approval time of 5.2 days. Is this evidence that the mean time to approval is not as advertised? To answer this, we test the following hypotheses at the a=0.05 level: H0: m = 5, Ha: m is not equal to5.
We find that the test statistic is z = 3. What is the p-value for this test?

Question 24
Suppose Math SAT scores for seniors in a school district are Normally distributed with a standard deviation of 100. Suppose a random sample of 25 seniors from this district is selected and their SAT scores have a mean of 450. A 95% confidence interval for the true mean of these SAT scores has a margin of error

Question 25
The distribution of actual weights of 8 oz. wedges of cheddar cheese produced by a certain company is normal with
m=8.15 ounces and s=0.1 ounces. If a sample of four of these cheese wedges is selected, what is the probability that their average weight is less than 8 oz.?

Question 26
Here are 4 measurements for the electrical conductivity of an iron rod: 10.0, 9.9, 10.2, 10.2
The iron rod is supposed to have conductivity 10.1. We wish to test this against the alternative hypothesis that the conductivity is not 10.1. Given that this population of conductivities is known to have a Normal distribution with standard deviation of 0.1. What is the test statistic?

Question 27
A medical researcher treats 25 subjects with high cholesterol with a new drug. The average decrease in cholesterol level is 80 after two months of taking the drug. Assume that the decrease in cholesterol after two months of taking the drug follows a normal distribution, with unknown mean mand standard deviation s= 20.
Find a 85% confidence interval for m.

Question 28
The distribution of actual weights of 8 oz. wedges of cheddar cheese produced by a certain company is Normally distributed with m =8.15 ounces and s = 0.1 ounces. A sample of four of these cheese wedges is selected. If a wedge is chosen from this population what is the probability that it weighs less than 8 ounces?

Question 29
Suppose the time that it takes a certain large bank to approve a home loan is normally distributed with mean (in days) m and standard deviation s = 1. The bank advertises that it approve loans in 5 days, on average, but measurements on a random sample of 100 loan applications to this bank gave a mean approval time of 5.2 days. Is this evidence that the mean time to approval is actually more than advertised? To answer this, we test the following hypotheses at the a=0.05 level: H0: m = 5, Ha: m> 5.
The P-value for this test is

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