# Mathematics

Chapter 6 Test

Question 1 For a normal distribution curve with a mean of 17 and a standard deviation of 3, which range of the variable defines an area under the curve corresponding to a probability of approximately 68%? a. from 15.5 to 18.5 b. from 14 to 20 c. from 17 to 23 d. from 11 to 23

Question 2 Find the probability P (z< 0.17) using the standard normal distribution. a. 0.8300 b. 0.4325 c. 0.5675 d. 0.0675

Question 3 Find the probability P (z<−0.46) using the standard normal distribution. a. 0.6772 b. 0.3228 c. 0.8228 d. 0.5400

Question 4 Find the probability P (z>−0.74) using the standard normal distribution. a. 0.2296 b. 0.7704 c. 0.7296 d. 0.2704

Question 5 Find the probability , P (0<z<1.67) using the standard normal distribution. a. 45.25% b. 45.54% c. 42.07% d. 35.54%

Question 6 Find the probability P (0.26< z< 1.33) using the standard normal distribution. a. 0.3057 b. 0.6943 c. 0.8057 d. 0.4600

Question 7 Find the probability P (−0.67< z<−0.06) using the standard normal distribution. a. 0.1400 b. 0.7754 c. 0.3546 d. 0.2246

Question 8 Find the probability P (−0.94< z< 1.21) using the standard normal distribution. a. 0.8367 b. 0.2867 c. 0.7133 d. 0.6701

Question 9 In a standard normal distribution, what z value corresponds to 17% of the data between the mean and the z value? a. 1.25 b. 0.44 c. 0.52 d. 2.10

Question 10 For a normal distribution with a mean of 7 and a standard deviation of 4, the value 13 has a z value of a. –1.5 b. 1.5 c. 2.5 d. 3.5

Question 11 If a normally distributed group of test scores have a mean of 70 and a standard deviation of 12, find the percentage of scores that will fall below 50 a.4.75% b. 45.25% c. 6.75% d. 35.54%

Question 12 The average height of flowering cherry trees in a certain nursery is 9.5 feet. If the heights are normally distributed with a standard deviation of 1.3 feet, find the probability that a tree is less than 11.5 feet tall. a. 0.82 b. 0.94 c. 0.97 d. 0.88

Question 13 The average length of crocodiles in a swamp is 11.5 feet. If the lengths are normally distributed with a standard deviation of 1.7 feet, find the probability that a crocodile is more than 11 feet long. a. 0.88 b. 0.38 c. 0.12 d. 0.62

Question 14 The average gas mileage of a certain model car is 29.0 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 0.6 miles per gallon, find the probability that a car has a gas mileage of between 28.8 and 29.2 miles per gallon. a. 0.261 b. 0.239 c. 0.321 d. 0.131

Question 15 At a large department store, the average number of years of employment for a cashier is 5.7 with a standard deviation of 1.8 years, and the distribution is approximately normal. If an employee is picked at random, what is the probability that the employee has worked at the store for over 10 years? a. 99.2% b. 49.2% c. 1.7% d. 0.8%

Question 16 In order to be accepted into a certain top university, applicants must score within the top 5% on the SAT exam. Given that the exam has a mean of 1000 and a standard deviation of 200, what is the lowest possible score a student needs to qualify for acceptance into the university? a. 1400 b. 1330 c. 1250 d. 1100

Question 17 If the standard deviation of a normally distributed population is 56.0 and we take a sample of size 16, then the standard error of the mean is a. 14.0 b. 4.0 c. 56.0 d. 3.5

Question 18 The average age of vehicles registered in the United States is 96 months. Assume the population is normally distributed with a standard deviation of 15 months. Find the probability that the mean age of a sample of 36 vehicles is between 98 and 100 months? a. 44.5% b. 28.8% c. 15.7% d. 6.4%

Question 19 The average age of doctors in a certain hospital is 50.0 years old. Suppose the distribution of ages is normal and has a standard deviation of 4.0 years. If 16 doctors are chosen at random for a committee, find the probability that the average age of those doctors is less than 50.3 years. Assume that the variable is normally distributed. a. 11.8% b. 38.2% c. 53.8% d. 61.8%

Question 20 The mean weight of loads of rock is 51.0 tons with a standard deviation of 12.0 tons. If 25 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 50.0 tons. Assume that the variable is normally distributed. a. 15.91 b. 34.09 c. 65.91 d. 84.09

Question 21 The average number of mosquitoes in a stagnant pond is 80 per square meter with a standard deviation of 12. If 16 square meters are chosen at random for a mosquito count, find the probability that the average of those counts is more than 83.0 mosquitoes per square meter. Assume that the variable is normally distributed. a. 0.3% b. 15.9% c. 34.1% d. 84.1%

Question 22 The length of country and western songs is normally distributed and has a mean of 200 seconds and a standard deviation of 30 seconds. Find the probability that a random selection of 9 songs will have mean length of 186.30 seconds or less. Assume the distribution of the lengths of the songs is normal. a. 0.91 b. 0.41 c. 0.09 d. 0.59

Question 23 A biologist estimates that 80% of the deer in a region carry a certain type of tick. For a sample of 300 deer selected at random, what is the chance that 246 or fewer deer have this tick? a. 0.864 b. 0.826 c. 0.652 d. 0.174

Question 24 A magazine reported that 6% of American drivers admit to reading the newspaper while driving. If 500 drivers are selected at random, find the probability that exactly 40 will admit to reading the newspaper while driving.

a. 4.7% b. 2.0% c. 1.3% d. 0.6%

Question 25 If a baseball player’s batting average is 0.340 (i.e., the probability of getting a hit each time at bat is 0.340), find the probability that the player will have a bad season and get at most 60 hits in 200 times at bat? a. 38.3% b. 11.7% c. 36.9% d. 13.1%