Unit Test

A normal distribution of data has a mean of 90 and a standard deviation of 18. What is the approximate z-score for the value 64?

-1.4

A gymnastics coach records the scores of a gymnast and develops the probability distribution below. What is the probability the gymnast scores a 9 or 9.5?

0.14

The times of all 15 year olds who run a certain race are approximately normally distributed with a given mean µ= 18 sec and standard deviation σ= 1.2 sec. What percentage of the runners have times less than 14.4 sec?

0.15%

When finding the margin of error for the mean of a normally distributed population from a sample, what is α, assuming a confidence level of 74%?

0.26

The number of absences for one week for all students at a high school were compiled, and the probability distribution below was created. What is the probability in any given week that a randomly selected student will be absent no more than one day?

0.92

A scientist calculated the mean and standard deviation of a data set to be µ=120 and σ=9. She then found that she was missing one data value from the set. She knows that the missing data value was exactly 3 standard deviations away from the mean. What was the missing data value?

147

The proportions of multiple samples of registered voters who vote are normally distributed, with a mean proportion of 0.38 and a standard deviation of 0.0485. What is the probability that a sample chosen at random has a proportion of registered voters who vote between 0.37 and 0.39? Use the portion of the standard normal table below to help answer the question.

17%

The set of life spans of an appliance is normally distributed with a mean µ= 48 months and a standard deviation σ= 8 months. What is the life span of an appliance that has a z-score of -3?

24 months

The life spans of a computer manufacturer's hard drives are normally distributed, with a mean of 3 years 6 months and a standard deviation of 9 months. What is the probability of a randomly selected hard drive from the company lasting between 2 years 3 months and 3 years 3 months? Use the portion of the standard normal table below to help answer the question.

32%

A city's annual rainfall totals are normally distributed, and the probability that the city gets more than 43.2 inches of rain in a year is given by P(z≥1.5)=0.0668. If the standard deviation of the city's yearly rainfall totals is 1.8 inches, what is the city's mean annual rainfall?

40.5 inches

Which set of population data is the least dispersed from its mean?

6, 2, 2, 2

The times taken to assemble a clock at a factory are approximately normally distributed with a given mean µ= 3 hr and standard deviation σ = 0.5 hr. What percentage of the times are between 2 hr and 4 hr?

95%

The grades of a science test are normally distributed. Thanh finds that his grade on the test has a z-score of -2.5. Which statement must be true?

Thanh's grade is 2.5 standard deviations below the mean of the test grades.

What is the formula for margin of error?

ME=z×s over √n

Opal is collecting data on water levels in different parts of town. She notices that her sample data has a low-value outlier. Which statement must be true?

Removing the outlier will decrease the spread of the graph of the data set.

The histogram below shows the number of weeks Jimmy spent different amounts of money to fill the gas tank in his car.

The difference in the heights of the bars will not appear as great.

The histogram below shows the estimated monthly salaries of company employees with different years of experience.How might the graph be misleading?

The scale on the y-axis overemphasizes the difference in salaries between different experience levels.

Veronique has a spinner with three sections of equal size, red (r), green (g), and blue (b).The spinner is spun twice. The sample space for the possible outcomes is S = {rr, rb, rg, gr, gg, gb, br, bg, bb}. If the number of times red is spun is the random variable, X, which graph represents the probability distribution?

a - the top graph

A simple random sample of size n is drawn from a normally distributed population, and the mean of the sample is x, while the standard deviation is s. What is the 90% confidence interval for the population mean? Use the table below to help you answer the question.

x=1.645×s over √n

A supervisor finds the mean number of miles that the employees in a department live from work. He finds mc022-1.jpg and mc022-2.jpg. Which statement must be true?

z37 is between 2 and 3 standard deviations of the mean.