Name: ______________________________________________ 5) Consider the following two normal curves: AP Statistics AP Review – Continuous Distributions 1) If 75% of all families spend more than $75 weekly for food, while 15% a b spend more than $150, what is the mean weekly expenditure and what is the standard deviation? Assume a normal distribution. a) = 83.33, = 12.44 d) = 104.39, = 43.86 Which has the larger mean and which has the larger standard deviation? b) = 56.26, = 11.85 e) = 139.45, = 83.33 a) Larger mean a; larger standard deviation a c) = 118.52, = 56.26 b) Larger mean a; larger standard deviation b c) Larger mean b; larger standard deviation a d) Larger mean b; larger standard deviation b 2) The income per household in a certain state is normally distributed e) Larger mean b; same standard deviation with a mean $9500 and a standard deviation of $1750. The middle 95% of incomes are between what two values? a) $5422 and $13,578 d) $7260 and $11,740 6) Which of the following statements is false? b) $6070 and $12,930 e) $8049 and $10,951 a) In all normal distributions, the mean and the median are equal. c) $6621 and $12,379 b) All bell-shaped curves are normal distributions for some and . c) Virtually all the area under a normal curve is within three standard deviations, no matter what the particular and are. 3) The noise level in a restaurant is normally distributed with an average d) For all normal curves, there is approximately a 95% chance that an of 30 decibels and a standard deviation of 4 decibels. Ninety-nine observation will be within 2 standard deviations of the mean. percent of the time it is below what value? e) The fiftieth percentile of a normal distribution is the mean of the a) 20.7 d) 37.8 distribution. b) 32.0 e) 39.3 c) 33.4 7) A z-score is called a standardized score because you can a) translate any x-value into a z-score. 4) An electronic product takes an average of 3.4 hours to move through b) translate any x-value from a normal distribution into a z-score. an assembly line. If the time is normally distributed with a standard c) translate z-scores into a proportion, a percentile, or a probability of deviation of 0.5 hour, what is the probability that an item will take the normal curve. between 3 and 4 hours to go through the line? d) use z-scores to find the area between a z-score and the mean, or the a) .2119 d) .3811 area below a z-score. b) .2295 e) .6730 e) use them to compare x-values to a universal standard, in this case, the c) .3270 standard normal distribution. 8) Suppose the grades on the last AB Calculus quiz are uniformly 12) Which of the following is the least likely to fit a normal distribution? distributed with a range of 46 and a median of 72. What is the a) Distribution of heights of professional soccer players probability that a randomly selected student did not pass? b) Distribution of the weights of salmon in the Pacific Ocean a) .4565 d) .5 c) Distribution of test scores among those who took the SAT in 2003 b) .5435 e) 1.52 d) Distribution of the ages of automobiles in drivable condition c) .9130 e) Distribution of the points scored by a basketball player per game 9) Which of the following is true about the areas described under the 13) You have two normally distributed populations: normal curve? Population A: = 50 and= 12 a) The area below the mean is greater than the area above the mean. Population B: = 75 and= 15 b) The area in the range from z = 0 to z = 1 is the same as the area in Which of the following has the greatest area? the range from z = 1 to z = 2. a) Area below 25 in Population A c) Roughly 50% of the observations are located at the mean of the b) Area above 65 in Population A distribution. c) Area between 75 and 90 in Population B d) Fewer than 1% of the observations are three standard deviations d) Area below 60 in Population B above or below the mean. e) Area above 80 in Population B e) 95% of the observations have values twice that of the mean. 14) All the following would be evidence that you do not have a normal 10) Suppose the density curve at the right distribution, except represents the GPAs of PWSH students, what .3 a) the presence of multiple modes. is the probability that a randomly selected .2 b) the fact that 75% of the observations have a value below the mean. student will have a GPA over 2.5? .1 c) a normal probability plot suggest an obviously curved line. a) .5 d) .75 d) the likelihood for all values of x is the same. 1 2 3 4 5 b) .625 e) .25 e) None of the above. c) .375 15) Assume that a baseball team has an average pitcher, that is, one 11) Which of the following statements about a uniform distribution is whose probability of winning any game is .5. If this pitcher has 30 games false? in a season, what is the probability that he will win at least 20 games? a) The area below the mean is greater than the area above the mean. a) .0505 d) .3333 b) The area in the range from z = 0 to z = 1 is the same as the area in b) .2514 e) .4300 the range from z = 1 to z = 2. c) .2743 c) The mean and median are always equal. d) If the range is 10, then the minimum x-value is located 5 units below the mean. e) The height of the distribution is calculated using 1/range.
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