Unit Test — Unit test Answers

Hal and Jose are avid crossword puzzle solvers. Hal solves 48% of his crossword puzzles in under 30 minutes, while Jose solves 39% of his crossword puzzles in under 30 minutes. Suppose that Hal solves 22 crossword puzzles and Jose solves 26 crossword puzzles. Because nJpJ, nJ (1–pJ), and nH (1-pH) are all greater than 10, the Normal condition is met. Let H = the proportion of Hal’s crossword puzzles solved in under 30 minutes and J = the proportion of Jose’s crossword puzzles solved in under 30 minutes. What is the probability that Jose’s proportion of crossword puzzles solved in under 30 minutes is greater than Hal’s?Find the z-table here.

The prices of houses in the US is strongly skewed to the right with a mean of $383,500 and a standard deviation of $289,321. A real estate agent takes a random sample of 30 houses and records the mean price. What is the best description for the sampling distribution?

The prices of pants at a large clothing store chain are skewed left with a mean of $32 and a standard deviation of $20. The manager at one of the stores randomly selects 30 pairs of pants. What is the shape of the distribution of the sample mean for all possible random samples of size 30 from this population?

A catering company provides packages for weddings and for showers. The cost per person for small groups is approximately Normally distributed for both weddings and showers. The mean cost for weddings is $82.30 with a standard deviation of $18.20, while the mean cost for showers is $65 with a standard deviation of $17.73. If 9 weddings and 6 showers are randomly selected, what is the probability the mean cost of the weddings is more than the mean cost of the showers?

A bottled water company bottles varying sizes of water, from 8-ounce to 1-gallon containers. The company has determined that the mean quantity in their 20-ounce bottles is 20.8 ounces with a standard deviation of 0.6 ounces. The bottling plant manager believes his machines are overfilling the bottles. A random sample of 30 bottles is taken, and the mean number of ounces of water is determined to be 21. Under the assumption that the true mean ounces of water is 20.8, 100 simulated means for samples of size 30 are shown in the dotplotWhat does the dot above 21 represent?

A conference consists of 5 sessions: A, B, C, D, and E. Here are the costs of the sessions.Session A: $50Session B: $50Session C: $100Session D: $150Session E: $200Here is a graph of the cost of all 5 sessions.A participant plans to attend 3 sessions. Here is a list of all possible samples of size 3 sessions from this population of 5 sessions: ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, and CDE.Here is a graph displaying the minimum session cost for each possible sample of 3 sessions.The participant chooses 3 sessions at random from the list of all 5 sessions. The result of the random selection is sessions B, D, and E.Here is a graph displaying the distribution of session cost for this sample.

In a large high school, 37% of the teachers believe that five minutes is not enough time for students to change classes. However, 89% of the students believe that five minutes is not enough time for students to change classes. Let and be the sample proportions of teachers and students, respectively, who believe that five minutes is not enough time for students to change classes. Suppose 28 teachers and 100 students are selected at random and asked their opinion on the amount of time students have to change class.Which of the following is the mean of the sampling distribution of ?

The times to pop a regular bag of microwave popcorn without burning it are Normally distributed with a mean time of 140 seconds and a standard deviation of 20 seconds. The times to pop a mini bag of microwave popcorn, without burning it, are Normally distributed with a mean time of 90 seconds and a standard deviation of 15 seconds. Suppose two independent random samples, 25 of each, are taken and the mean popping times are calculated. Let R = the popping time of a randomly selected regular-sized bag and M = the popping time of a mini-sized bag. Which of the following best describes the mean of the sampling distribution of ?

A veteran math teacher at a large high school claims that 93% of their students pass the state’s final exam. A random sample of 120 of the teacher’s students was chosen, and 108 passed the state’s final exam. Let = the proportion of the random sample who passed the state’s final exam.The probability that 90% or fewer of this teacher’s students passed the state’s final exam is 0.096. Does this result provide convincing evidence against the teacher’s claim?

A student would like to estimate the mean length of words in a book report he just finished writing. He selects a random sample of 20 words and determines the mean length to be 4 characters. Later, he discovers how to use a built-in function of his word-processing program that reveals that the mean length of all words in his book report is 4.3 characters. Which of the following describes the number, 4.3?

A cell phone provider has 85% of its customers rank their service as "satisfactory.” Nico takes a random sample of 75 customers from this cell phone provider. What is the probability that 83% or more of this sample ranks the provider’s service as "satisfactory”?Find the z-table here.

The weights of bunches of bananas in the grocery store are Normally distributed with a mean weight of 3.54 pounds and a standard deviation of 0.64 pounds. A random sample of four bunches is taken and the mean weight is recorded. Which of the following is the standard deviation of the sampling distribution for the mean of all possible samples of size four?

The ages of the 5 officers for a school club are 18, 18, 17, 16, and 15. The minimum of the ages of the officers is 15. The table displays all possible samples of size 2 and the corresponding minimum for each sample.Using the minimums in the table, is the sample minimum an unbiased estimator?

In a large high school, 37% of the teachers believe that five minutes is not enough time for students to change classes. However, 89% of the students believe that five minutes is not enough time for students to change classes. Let and be the sample proportions of teachers and students, respectively, who believe that five minutes is not enough time for students to change classes. Suppose 28 teachers and 100 students are selected at random and asked their opinion on the amount of time students have to change class.Which of the following is the correct shape and justification of the sampling distribution of ?

An air-conditioning repair technician claims to complete 67% of repairs in under an hour. A random sample of 31 repairs was chosen, and 22 of those were completed in under an hour. Let = the proportion of the random sample that were completed in under an hour.The probability that 71% or more of this technician’s repairs were completed in under an hour is 0.317. Does this result provide convincing evidence against the technician’s claim?