ME 430 Chapter 9
The weights of male basketball players on a certain campus are normally distributed with a mean of 180 pounds and a standard deviation of 26 pounds. If a player is selected at random, the probability that the player will weigh more than 225 pounds is (a) 0.0418 (b) 0.4582 (c) 0.9582 (d) 0.5418
(a) 0.0418
Suppose that family incomes in a town are normally distributed with a mean of $1,200 and a standard deviation of $600 per month. The probability that given family has an income over $2,000 per month is (a) 0.0918 (b) 0.9082 (c) 0.4082 (d) 0.5918
(a) 0.0918
The time it takes a driver to react to the brake lights on a decelerating vehicle is normally distributed with a mean of 1.30 seconds and standard deviation of 0.3 seconds. What is the probability that the reaction time of a driver is less than 1.00 seconds? (a) 0.1587 (b) 0.4514 (c) 0.7257 (d) 0.5486
(a) 0.1587
The waiters in a restaurant receive an average tip of $20 per table with a standard deviation of $5. The amounts of tips are normally distributed, and management of the restaurant has established that a waiter has provided excellent service if the tip is more than $25. The probability that a waiter has provided excellent service to a table is (a) 0.1587 (b) 0.8413 (c) 0.8000 (d) 0.6587
(a) 0.1587
The manager of a local cell phone store believes that the annual revenue of the store can approximated by a normal distribution with a mean of $250,000 and a standard deviation of $30,000. If this is the model the manager is using to predict next year's total revenue, then the probability that the total sales will be greater than the mean by at least $10,000 is (a) 0.3694 (b) 0.6293 (c) 0.1293 (d) 0.4059
(a) 0.3694
The area under the standard normal curve between z = -1.68 and z = 0 is (a) 0.4535 (b) 0.0465 (c) 0.9535 (d) -0.4535
(a) 0.4535
A company that bottles apple juice has a machine that automatically fills 12-ounce bottles. From quality control data it was found that the average amount of apple juice dispensed into the bottles was 12 ounces with a standard deviation of 0.5 ounces. If a bottle is chosen at random from the production line, what is the probability that the machine will overfill the bottle if the amount dispensed is assumed to be normally distributed? (a) 0.5000 (b) 0.1587 (c) 0.0000 (d) 0.8413
(a) 0.5000
The area under any normal curve that is within two standard deviations of the mean is approximately (a) 0.950 (b) 0.680 (c) 0.997 (d) 0.500
(a) 0.950
The value of z_0 such that P(z<=z_0) = 0.8997 is (a) 1.28 (b) 0.00 (c) 0.1003 (d) none of the above
(a) 1.28
The systolic blood pressure of adults is approximately normally distributed with a mean of 128 and a standard deviation of 20. Give an interval in which the blood pressures of approximately 95 percent of the population will fall. (a) 88 to 168 (b) 68 to 188 (c) 108 to 148 (d) 88 to 188
(a) 88 to 168
The specification for the diameter of a steel washer is set by the buyer to be 2 +- 0.01 cm. Any washer with a diameter outside of this specification will be scrapped. What percentage of the washers will be accepted if the diameter is normally distributed with a mean of 2 cm and standard deviation of 0.005 cm? (a) 95.45 percent (b) 2.275 percent (c) 97.725 percent (d) 4.55 percent
(a) 95.45 percent
A statistics professor has established that the final overall percentage per student in her elementary statistics course is normally distributed with a mean and standard deviation of 79 and 7 respectively. If the professor decides to assign her grades, for this current semester, based on a curve such that only the bottom 10 percent of her students receive a failing grade, then the cutoff percentage to earn a failing grade is (a) less than or equal to 70.03 (b) less than or equal to 65.00 (c) less than or equal to 71.10 (d) less than or equal to 63.20
(a) less than or equal to 70.03
The two z values such that the area bounded by them is equal to the middle 68.26 percent of the standard normal distribution is (a) +- 3 (b) +- 1 (c) +- 2 (d) +- 1.96
(b) +- 1
If X is a normal random variable with a mean of 15 and a variance of 9, then P(X=18) is (a) 0.8413 (b) 0.0000 (c) 0.3413 (d) 0.1587
(b) 0.0000
A bank finds that the balances for its customers in their savings accounts are normally distributed with a mean of $500 and a standard deviation of $50. The probability that a randomly selected account has a balance more than $600 is (a) 0.4772 (b) 0.0228 (c) 0.9772 (d) 0.0000
(b) 0.0228
If X is a normally distributed random variable with a mean of 6 and a variance of 4, then the probability that X is greater than 10 is (a) 0.1587 (b) 0.0228 (c) 0.6587 (d) 0.5228
(b) 0.0228
The life of a brand of battery is normally distributed with a mean of 62 hours and a standard deviation of 6 hours. The probability that a single randomly selected battery will last more than 70 hours is (a) 0.0000 (b) 0.0918 (c) 0.4082 (d) 0.9082
(b) 0.0918
The area under the standard normal curve between -2.0 and -1 is (a) 0.0228 (b) 0.1359 (c) 0.4772 (d) 0.3413
(b) 0.1359
The length of time it takes to find a parking spot during the summer terms on campus follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute. The probability that a student attending classes during the summer terms will take more than 3 minutes to find a parking spot is (a) 0.8085 (b) 0.6915 (c) 0.3085 (d) 0.1915
(b) 0.6915
If X is a normal random variable with a mean of 15 and a variance of 9, then P(X<18) is (a) 0.7486 (b) 0.8413 (c) 0.3413 (d) 0.1587
(b) 0.8413
The waiters in a bar receive an average tip of $20 per table with a standard deviation of $5. The amounts of tips are normally distributed, and a waiter feels that he has provided excellent service if the tip is more than $25. The probability that a waiter has not provided excellent service (according to the waiters' theory) to a table is (a) 0.1587 (b) 0.8413 (c) 0.8000 (d) 0.6587
(b) 0.8413
The weights of male basketball players on a certain campus are normally distributed with a mean of 180 pounds and a standard deviation of 26 pounds. If a player is selected at random, the probability that the player will weigh less than 225 pounds is (a) 0.5418 (b) 0.9582 (c) 0.4582 (d) 0.0418
(b) 0.9582
If X is a normally distributed random variable with a mean of 6 and a variance of 4, then the probability that X is less than 10 is (a) 0.8413 (b) 0.9772 (c) 0.3413 (d) 0.4772
(b) 0.9772
Suppose that family incomes in a town are normally distributed with a mean of $1,200 and a standard deviation of $600 per month. The probability that given family has an income between $1,000 and $2,050 per month is (a) 0.4585 (b) 0.7001 (c) 0.4222 (d) 0.5515
(d) 0.5515
The probability that an observation taken from a standard normal population will be between -1.96 and 1.28 is (a) 0.0753 (b) -0.0753 (c) 0.1253 (d) 0.8747
(d) 0.8747
The average score on one of your statistics examination was 75 with a standard deviation of 10. If your corresponding z score was 2, then your corresponding raw score and percentile rank (approximate) would be (a) 55; 48 percent (b) 65; 12 percent (c) 85; 75 percent (d) 95; 98 percent
(d) 95; 98 percent
If Z is a standard normal random variable, which of the following statements is correct? (a) P(Z>-2.5) = P(Z>2.5) (b) P(Z>-2.5) = P(Z<-2.5) (c) P(Z>-2.5) = P(-2<Z<2.5) (d) P(Z>-2.5) = P(Z<2.5)
(d) P(Z>-2.5) = P(Z<2.5)
For any z distribution, the sum of all the associated z scores always will be (a) equal to 1 (b) less than 1 (c) greater than 1 (d) equal to 0
(d) equal to 0
If the z score associated with a given raw score is equal to 0, this implies that (a) the raw score equals 0 (b) the raw score does not exist (c) the raw score is extremely large (d) the raw score is the same as the mean
(d) the raw score is the same as the mean
In a normal distribution, the distribution will be less spread out when (a) the mean of the raw scores is small. (b) the median of the raw scores is small (c) the mode of the raw scores is small (d) the standard deviation of the raw scores is small
(d) the standard deviation of the raw scores is small
A random variable that can assume any value in the set of real numbers must be normally distributed.
False
A z value of 1 indicates that 1 percent of the area under the standard normal curve is to the right of the z value of 0.
False
Because of the right and left tails of the normal curve, we can say that the normal distribution is skewed to both the left and right.
False
Continuous random variables typically arise from counting some type of quantity.
False
If X is a normal random variable, the P(X>0) = 0.5 is always true.
False
If the computed z value is negative, you definitely have made a computational error.
False
Not all normal distributions can be transformed to a standard normal distribution.
False
The area under the normal curve left of its mean is -0.5.
False
The probability that a continuous random variable assumes any single value always will be nonzero.
False
The total area under the normal curve is approximately 1.
False
The z value or z score is computed from the equation z = (mu-x)/sigma, where x is the value of a normal random variable X with mean mu and standard deviation sigma.
False
Which of the following situations may not require a z score to be computed? (a) A college basketball player wants to know the probability that he will get more than 72 percent of his 3-point shots based on his performance during the last two seasons. (b) A college baseball player wants to know the median batting average for his team during the last season. (c) A college softball player wants to know the minimum batting average that she would have to achieve to be in the top 10 percent of her team. (d) A statistics professor wants to "curve" the overall average for his course such that the bottom 5 percent of the students in his class will receive a failing grade.
(b) A college baseball player wants to know the median batting average for his team during the last season.
Which of the following is not needed in computing the z score for a normal random variable? (a) The value of the raw score (b) The percentile rank of the raw score (c) The standard deviation for the random variable (d) The mean score for the random variable
(b) The percentile rank of the raw score
A standard normal distribution is a normal distribution with (a) mu = 1 and sigma = 0 (b) mu = 0 and sigma = 1 (c) any mean and sigma = 0 (d) any mean and any standard deviation
(b) mu = 0 and sigma = 1
The time it takes a driver to react to the brake lights on a decelerating vehicle is normally distributed with a mean of 1.30 seconds and standard deviation of 0.3 seconds. If the reaction time is more than 2 seconds, a rear-end collision is likely to occur in heavy traffic. What is the probability of a rear-end collision in heavy traffic? (a) 0.9192 (b) 0.4192 (c) 0.0096 (d) 0.8385
(c) 0.0096
The weights of male basketball players on a certain campus are normally distributed with a mean of 180 pounds and a standard deviation of 26 pounds. If a player is selected at random, the probability that the player will weigh between 180 and 225 pounds is (a) 0.5000 (b) 0.5418 (c) 0.4582 (d) 0.9582
(c) 0.4582
The life of a brand of battery is normally distributed with a mean of 62 hours and a standard deviation of 6 hours. The probability that a single randomly selected battery will last from 55 to 65 hours is (a) 0.4295 (b) 0.6875 (c) 0.5705 (d) 0.3125
(c) 0.5705
The time it takes a driver to react to the brake lights on a decelerating vehicle is normally distributed with a mean of 1.30 seconds and standard deviation of 0.3 seconds. What is the probability that the reaction time of a driver is between 1.00 and 1.50 seconds? (a) 0.3893 (b) 0.2743 (c) 0.5889 (d) 0.8849
(c) 0.5889
The manager of a local crafts store believes that the yearly revenue of the store can be approximated by the normal distribution with a mean of $250,000 and a standard deviation of $40,000. If this is the model the manager is using to predict next year's revenue and the break-even revenue is $180,000 (this is the total cost to run the business for one year), then the probability that the store will make a profit is (a) 0.4599 (b) 0.9198 (c) 0.9599 (d) 0.0401
(c) 0.9599
The scores on a standardized test are normally distributed with a mean of 400 and a standard deviation of 100. If a certain university will only consider applicants with scores in the upper 10 percent, what is the minimum score required for consideration at this university? (a) 450 (b) 500 (c) 529 (d) 600
(c) 529
The speeds of cars traveling on Kentucky's highways are normally distributed with a mean 60 mph and a standard deviation 5 mph. If Kentucky's police follow a policy of not ticketing the slowest 90 percent, at what speed will the police start to issue tickets? (Round up all answers to the next whole number.) (a) 54 mph (b) 52 mph (c) 66 mph (d) 68 mph
(c) 66 mph
Which of the following does not apply to the normal distribution? (a) The normal curve is unimodal (b) The total probability under the curve is 1 (c) The normal curve is symmetrical about its standard deviation (d) The mean, the median, and the mode are all equal to each other
(c) The normal curve is symmetrical about its standard deviation
The two z values such that the area bounded by them is equal to the middle 90 percent of the standard normal distribution is (a) +- 1.640 (b) +- 1.650 (c) +- 2.000 (d) +- 1.645
(d) +- 1.645
For the standard normal random variable z, P(z = 0) is (a) 0.5 (b) less than 0.5 (c) same as P(-0.5<=z<=0.5) (d) 0
(d) 0
If IQ scores are normally distributed with a mean of 100 and a standard deviation of 20, then the probability of a person's having an IQ score of at least 130 is (a) 0.4332 (b) 0.3000 (c) 0.9332 (d) 0.0668
(d) 0.0668
The time it takes for a dose of a certain drug to be effective as a sedative on laboratory animals is normally distributed with a mean of 1 hour and a standard deviation of 0.1 hour. If X represents this time, then P(X>1.1) is (a) 0.0000 (b) 0.5000 (c) 0.3643 (d) 0.1587
(d) 0.1587
If z is a standard normal random variable, then the probability that z>1 or z<-2 is (a) 0.1587 (b) 0.0228 (c) 0.8185 (d) 0.1815
(d) 0.1815
The lifetime of a certain brand of tires is normally distributed. The average lifetime of a tire is 50,000 miles with a lifetime standard deviation of 8,400 miles. The probability that a randomly selected tire will last beyond 55,000 miles is (a) 0.2257 (b) 0.7257 (c) 0.0000 (d) 0.2743
(d) 0.2743
The manager of a local cell phone store believes that the yearly revenue of the store can be approximated by a normal distribution with a mean of $250,000 and a standard deviation of $30,000. If this is the model the manager is using to predict next year's revenue, then the probability that the total sales will be more than the mean by at least $10,000 is (a) 0.1293 (b) 0.8707 (c) 0.6306 (d) 0.3694
(d) 0.3694
The lifetime of a certain brand of tire is normally distributed with an average of 50,000 miles and a standard deviation of 8,400 miles. The probability that a randomly selected tire will last beyond 52,000 miles is (a) 0.6406 (b) 0.1406 (c) 0.2812 (d) 0.4059
(d) 0.4059
The U.S. Bureau of Census reports that the average annual alimony income received by women is $3,000 with a standard deviation of $7,500. If the annual alimony income is assumed to be normally distributed, then the proportion of women who receive less than $2,000 in annual alimony income is (a) -0.0517 (b) 0.5517 (c) 0.8966 (d) 0.4483
(d) 0.4483
A positive z score gives the number of standard deviations a specified value of a normal random variable is above its mean.
True
Approximately 68 percent of a normal population will lie within one standard deviation of its mean.
True
For any continuous random variable X, P(X>2)=P(X>=2).
True
The area under any normal curve between a and b gives the probability that the normal random variable lies between a and b.
True
The mean, the median and the mode for a normal distribution are all equal.
True
The normal distribution is centered at its mean.
True
The probability that a normal random variable X is at least some number a can be denoted as P(x>a).
True
The standard normal distribution has a mean of zero and a variance of 1.
True
The standard normal distribution is symmetrical about 0.
True
