Chapter 5 Review The Normal Probability and Standardization …

1 Chapter 5 Review The Normal Probability and Standardization MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) Approximately ____% of the area under the Normal curve is between - and + . 1). A) B) 95 C) 68 D) 50. A random variable X is normally distributed with = 60. Convert the value of X to a z-score, if the standard deviation is as given. 2) X = 72; = 3 2). A) 3 B) 5 C) 12 D) 4. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

2 Find the standard Normal -curve area indicated. 3) Between z = and z = 3). 4) To the left of z = 4). The number of ounces of soda that a vending machine dispenses per cup is normally distributed with a mean of 12. ounces and a standard deviation of 4 ounces. 5) Find the Probability that more than 16 ounces is dispensed in a cup. 5). 6) Find the Probability that between 15 and 18 ounces are dispensed in a cup. 6). 7) Find the number of ounces above which 80% of the dispensed sodas will fall. Round to the 7). nearest tenth. MULTIPLE CHOICE.

3 Choose the one alternative that best completes the statement or answers the question. A random variable X is normally distributed with = 60. Convert the value of X to a z-score, if the standard deviation is as given. 8) X = 30; = 8 8). A) -8 B) C) D) 8. 1. Obtain the shaded area under the standard Normal curve. 9) 9). z A) B) C) D) 10) 10). z A) B) C) D) 11) 11). z A) B) C) D) find the required z-score. 12) Find the z-score for which the area under the standard Normal curve to its left is 12). A) B) C) D) 13) Find the z-score having area to its right under the standard Normal curve; that is, find z.

4 13). A) B) C) D) Provide an appropriate response. 14) Scores on a standardized test are normally distributed with a mean of 96 and a standard deviation 14). of 12. An individual's test score is found to be 128. Find the z-score corresponding to this value. A) B) C) D) 2. find the required z-score. 15) Determine the two z-scores that divide the area under the standard Normal curve into a middle 15). area and two outside areas. A) 0 and B) and C) and D) and Provide an appropriate response. 16) Find the z-scores for which 98% of the distribution's area lies between -z and z.

5 16). A) ( , ) B) ( , ) C) ( , ) D) ( , ). 17) A physical fitness association is including the mile run in its secondary-school fitness test. The time 17). for this event for boys in secondary school is known to possess a Normal distribution with a mean of 440 seconds and a standard deviation of 60 seconds. Find the Probability that a randomly selected boy in secondary school can run the mile in less than 302 seconds. A) B) C) D) 18) A physical fitness association is including the mile run in its secondary-school fitness test. The time 18).

6 For this event for boys in secondary school is known to possess a Normal distribution with a mean of 470 seconds and a standard deviation of 50 seconds. Find the Probability that a randomly selected boy in secondary school will take longer than 355 seconds to run the mile. A) B) C) D) 19) The length of time it takes college students to find a parking spot in the library parking lot follows a 19). Normal distribution with a mean of minutes and a standard deviation of 1 minute. Find the Probability that a randomly selected college student will find a parking spot in the library parking lot in less than minutes.

7 A) B) C) D) 20) The tread life of a particular brand of tire is a random variable best described by a Normal 20). distribution with a mean of 60,000 miles and a standard deviation of 2500 miles. What is the Probability a particular tire of this brand will last longer than 57,500 miles? A) B) C) D) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 21) A firm believes the internal rate of return for its proposed investment can best be described 21). by a Normal distribution with mean 20% and standard deviation 3%.

8 What is the Probability that the internal rate of return for the investment will be at least 3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 22) A physical fitness association is including the mile run in its secondary-school fitness test. The time 22). for this event for boys in secondary school is known to possess a Normal distribution with a mean of 450 seconds and a standard deviation of 50 seconds. The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition.

9 What time would the boys need to beat in order to earn a certificate of recognition from the fitness association? A) sec B) 386 sec C) 514 sec D) sec 23) The amount of corn chips dispensed into a 16-ounce bag by the dispensing machine has been 23). identified as possessing a Normal distribution with a mean of ounces and a standard deviation of ounce. What chip amount represents the 67th percentile for the bag weight distribution? A) oz B) oz C) oz D) oz 24) The length of time it takes college students to find a parking spot in the library parking lot follows a 24).

10 Normal distribution with a mean of minutes and a standard deviation of 1 minute. Find the cut-off time which of the college students exceed when trying to find a parking spot in the library parking lot. A) min B) min C) min D) min Solve the problem. 25) A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric 25). energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $115 and a standard deviation of $12.