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A manager records the number of hours, X, each employee works on his or her shift and develops the probability distribution below. Fifty people work for the manager. How many people work 4 hours per shift?Probability DistributionHours Worked: XProbability: P(X)30.14?50.1460.370.3680.06

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Dwayne and Alisha both correctly graphed a standard normal curve. Which of the following statements is true?

Neither the means nor the standard deviations of Dwayne’s and Alisha’s graphs must be the same.

The means of Dwayne’s and Alisha’s graphs must be the same but not the standard deviations.

The standard deviations of Dwayne’s and Alisha’s graphs must be the same but not the means.

Both the means and the standard deviations of Dwayne’s and Alisha’s graphs must be the same.

A simple random sample of size n is drawn from a normally distributed population, and the mean of the sample is , while the standard deviation is s. What is the 99% confidence interval for the population mean? Use the table below to help you answer the question.Confidence Level90%95%99%z*-score1.6451.962.58

x Overbar plus-or-minus StartFraction 0.90 times s Over StartRoot n EndRoot EndFraction

x Overbar plus-or-minus StartFraction 0.99 times s Over StartRoot n EndRoot EndFraction

x Overbar plus-or-minus StartFraction 1.645 times s Over StartRoot n EndRoot EndFraction

x Overbar plus-or-minus StartFraction 2.58 times s Over StartRoot n EndRoot EndFraction

The scores of the students on a standardized test are normally distributed, with a mean of 500 and a standard deviation of 110. What is the probability that a randomly selected student has a score between 350 and 550? Use the portion of the standard normal table below to help answer the question.zProbability0.000.50000.250.59870.350.63680.450.67361.000.84131.260.89611.350.91151.360.9131

24%

59%

91%

The stem-and-leaf plot below shows the number of pages each student in a class read the previous evening.Which statement is true about the data set?

Its median is greater than its mode.

It has a range of 52 pages.

The value of the first quartile is 13.

The data is symmetric.

The mean test scores with standard deviations of four English classes are given below.ClassMeanStandard DeviationMrs. Jones891.9Mrs. Rijo821.4Mr. Phan733.4Mrs. Scott906.1Which statement is most likely to be true?

The scores of Mrs. Scott’s class are the closest to the class mean.

The scores of Mr. Phan’s class are the closest to the class mean.

The scores of Mrs. Jones’s class are the closest to the class mean.

The scores of Mrs. Rijo’s class are the closest to the class mean.

The graph below is used by company 2 to show the average monthly electric cost based on the electricity provider.How could the graph be redrawn so that the difference in monthly electric cost does not appear as great?

The scale on the y-axis could be changed to 0–150.

The scale on the y-axis could be changed to 100–120.

The interval on the y-axis could be changed to count by 1s.

The interval on the y-axis could be changed to count by 20s.

The mean of a set of credit scores is and . Which statement must be true about z694?

z694 is within 1 standard deviation of the mean.

z694 is between 1 and 2 standard deviations of the mean.

z694 is between 2 and 3 standard deviations of the mean.

z694 is more than 3 standard deviations of the mean.

The annual salaries of all employees at a financial company are normally distributed with a mean = $34,000 and a standard deviation = $4,000. What is the z-score of a company employee who makes an annual salary of $28,000?

–5

–3.5

–1.5

1.5

A convenience sample differs from a voluntary sample in that

a convenience sample is structured based on accessibility to the researcher, and a voluntary sample is based on participant interest.

convenience samples survey each participant once, and voluntary samples survey each participant numerous times.

convenience sampling is a method of random sampling, and a voluntary sample is not.

convenience sampling is not a probability-based method, and voluntary sampling is.

The resting heart rates for 80 women aged 46–55 in a simple random sample are normally distributed, with a mean of 71 beats per minute and a standard deviation of 6 beats per minute. Assuming a 90% confidence level (90% confidence level = z-score of 1.645), what is the margin of error for the population mean?Remember, the margin of error, ME, can be determined using the formula .

0.66

1.10

1.31

1.73

Destiny performs a hypothesis test on a population with µ = 115 and . Her sample size is 25 with a mean of 120.4. Which of the following correctly depicts the z-statistic for this data?

0.04

0.90

3.53

3.93

The difference between an observational study and an experiment is that

in an observational study, only one group is studied, and in an experiment, two groups are studied.

in an observational study, the researchers do not control treatment, and in an experiment, they do.

in an experiment, cause-and-effect is analyzed, and in an observational study, it is not.

in an experiment, one group is studied over a short period of time, and in an observational study, the group is studied over a longer period of time.

The graph below shows three different normal distributions.Which statement must be true?

Each distribution has the same mean and the same standard deviation.

Each distribution has the same mean and a different standard deviation.

Each distribution has a different mean and the same standard deviation.

Each distribution has a different mean and a different standard deviation.

Which of the following is a valid probability distribution?

Probability distribution A is shown. The probabilities of 1, 2, 3, 4, 5 and 6 are all 0.2.

Probability distribution B is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.3; 4 is 0.3; 5 is 0.2; 6 is 0.1.

Probability distribution C is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.4; 5 is 0.1; 6 is 0.1.

Probability distribution D is shown. The probability of 1 is 0.2; 2 is 0.1; 3 is 0.1; 4 is 0.5; 5 is 0.1.

A manager of a grocery store wants to determine if consumers are spending more than the national average. The national average is $150.00 with a standard deviation of $30.20. The manager collects 40 random receipts and finds that the average is $160. Complete a hypothesis test with a significance level of 2.5% to determine if the average customer spends more in his store than the national average. Which of the following is a valid conclusion for the manager based on this test?

The customers spend more than the national average in his store.

The manager should decrease prices in his store.

The customers do not spend more than the national average in his store.

The customers in his store just come from a rich neighborhood.

For a standard normal distribution, which of the following expressions must always be equal to 1?

P (z less-than-or-equal-to a) minus P (negative a less-than-or-equal-to z less-than-or-equal-to z) minus P (z greater-than-or-equal-to a)

P (z less-than-or-equal-to a) minus P (negative a less-than-or-equal-to z less-than-or-equal-to z) + P (z greater-than-or-equal-to a)

P (z less-than-or-equal-to a) + P (negative a less-than-or-equal-to z less-than-or-equal-to z) minus P (z greater-than-or-equal-to a)

P (z less-than-or-equal-to a) + P (negative a less-than-or-equal-to z less-than-or-equal-to z) + P (z greater-than-or-equal-to a)

The table below shows the ages of houses to the nearest year in a neighborhood. Using the age of the houses as the random variable, X, which graph shows the probability distribution, PX(x), of a randomly chosen house?Age of HouseNumber of Houses115220325430

A probability distribution is shown. The probability of 1 is 0.16; 2 is 0.22; 3 is 0.28; 4 is 0.33.

A probability distribution is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.3; 4 is 0.4.

A probability distribution is shown. The probability of 1 is 0.65; 2 is 0.1; 3 is 0.12; 4 is 0.13.

A probability distribution is shown. The probability of 1 is 0.15; 2 is 0.2; 3 is 0.25; 4 is 0.3.

To conduct a survey about the type of phone service most people in Greenville prefer, 10 different blocks in the neighborhood are chosen. On these 10 blocks, 10 houses are selected at random, and then each resident of each of those houses is interviewed. This type of sampling method is

simple random sampling.

stratified sampling.

systematic random sampling.

cluster sampling.

The hourly wages earned by 20 employees are shown in the first box-and-whisker plot below. The person earning $15 per hour quits and is replaced with a person earning $8 per hour. The graph of the resulting salaries is shown in plot 2.Plot 1 Plot 2 How does the mean and median change from plot 1 to plot 2?

The mean and median remain the same.

The mean decreases, and the median remains the same.

The mean remains the same, and the median decreases.

The mean and median decrease.

The histogram below represents the number of points Mandy scored per game. The graph makes the data appear symmetric when it is actually skewed. How can the graph be adjusted to show the skew?

The intervals on the x-axis can be changed to be continuous and consistent.

The interval on the y-axis can be changed to show only the relevant numbers, 3 and 5.

The scale on the x-axis can be increased to show the interval 25–29.

The scale on the y-axis can be decreased to show only the numbers 0–5.

A local weather enthusiast wants to see if the last five summers have been warmer than normal for Eloy, Arizona. From the National Oceanic and Atmospheric Administration (NOAA), he knows the 30-year average for July was 90° with a standard deviation of 2.1°. The last five summers recorded have an average of 93.5°. If he uses a = 5%, which of the following would be valid based on the data he has gathered?

He can conclude that the summers have been warmer than the 30-year average.

He can conclude that the summers will continue to be warmer for the next 10 years.

He does not have enough information to make a decision.

The average for the last five years fits with the 30-year average.

Emi computes the mean and variance for the population data set 87, 46, 90, 78, and 89. She finds the mean is 78. Her steps for finding the variance are shown below.What is the first error she made in computing the variance?

Emi failed to find the difference of 89 - 78 correctly.

Emi divided by N - 1 instead of N.

Emi evaluated (46 - 78)2 as -(32)2.

Emi forgot to take the square root of -135.6.

When finding the margin of error for the mean of a normally distributed population from a sample, what is the critical probability, assuming a confidence level of 58%?

0.21

0.42

0.58

0.79

In Juneau, Alaska, the 30-year annual snowfall average is 86.7 inches with a standard deviation of 40.4 inches. The last four years saw an average annual snowfall of 115.7 inches, 62.9 inches, 168.5 inches, and 135.7 inches. Hia performs a hypothesis test on this data to determine if the next 30-year norm will have a different average if the trend from the last four years continues. She uses a significance level of 5%. Which of the following is a conclusion that she may make?

The z-statistic is 1.44, so the null hypothesis cannot be rejected.

The z-statistic is 1.68, so the null hypothesis cannot be rejected.

The z-statistic is 1.85, so the null hypothesis should be rejected.

The z-statistic is 4.6, so the null hypothesis should be rejected.

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