Problem 1: Weight of Navel Oranges
Suppose that the weight of navel oranges is normally distributed with mean µ = 8 ounces, and standard deviation σ= 1.5 ounces. We can write X ~ N(8, 1.5). Answer the following questions:
(a) What proportion of oranges weigh more than 10.2 ounces?
(b) If you randomly select a navel orange, what is the probability that it weighs less than 6.9 ounces?
(c) What proportion of oranges weigh between 5.5 and 7 ounces?
(d) Find the 80th percentile of this distribution of X.
(e) Find the interquartile range of this distribution of X.
Problem 2: Z Scores from Table A
Use Table A to find the value z of a standard Normal variable that satisfies each of the following conditions. In each case sketch a standard Normal curve with your value of z marked on the axis.
(a) The point z with 35% of the observations falling below it.
(b) The point with 47% of the observations falling above it.
Problem 3: Wechsler Adult Intelligence Scale (WAIS) Scores
The scale of scores on the WAIS are approximately Normal with mean 100 and standard deviation 15.
Answer the following questions:
(a) The organization MENSA, which calls itself "the high-IQ society", requires an IQ score of 130 or higher for membership. What percent of adults would qualify for membership?
(b) Corrine scores 118 on such a test. How far away from the mean is she (or how many standard deviation units away from the mean is she)?
(c) Corrine scores higher than what percent of all adults?
(d) Individuals with WAIS scores below 70 are considered mentally retarded, when, for example, applying for Social Security disability benefits. By this criterion, what percentage of adults are retarded?
Problem 4: SAT versus ACT
There are two major tests of readiness for college: the SAT and the ACT. While ACT are reported on a scale from 1 to 36, SAT scores until recently was reported on a scale from 400 to 1600. The scores of ACT has a distribution that follows: N(20.9, 4.8) and SAT follows a distribution of N(1026, 209).
Answer the following questions:
(a) Maria scores 28 on the ACT. Assuming that both tests measure the same thing, what score on the SAT is equivalent to Maria's ACT score?
(b) Tonya scores 1318 on the SAT. What is her percentile?
(c) The quartiles of any distribution are the values with cumulative proportion 0.25, 0.50, and 0.75. What are the quartiles of the distribution of the ACT scores?
(d) The quintiles of any distribution are the values with cumulative proportion 0.20, 0.40, 0.60, and 0.80. What are the quintiles of the distribution of SAT scores?
(e) What SAT scores make up the 90th percentile?
(f) How well must Abigail do on the ACT in order to place in the top 1 percent?