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Liberty MATH 114 Homework 4 Answers Complete Solutions
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Question 1
Use the normal distribution of IQ scores, which has a mean of 90 and a standard deviation of 15, and the following table with the standard scores and percentiles for a normal distribution to find the indicated quantity.
Percentage of scores greater than 105 is
Question 2
The scores on a psychology exam were normally distributed with a mean of 65 and a standard deviation of 5. A failing grade on the exam was anything 2 or more standard deviations below the mean. What was the cutoff for a failing score? Approximately what percentage of the students failed?
The cutoff for a failing score was
Approximately percent of the students failed
Question 3
A set of data items is normally distributed with a mean of 180 and a standard deviation of 24. Convert 156 to a z-score.
Question 4
Use the accompanying table of standard scores and their percentiles under the normal distribution to find the approximate standard score of the following data values. Then state the approximate number of standard deviations that the value lies above or below the mean.
a. A data value in the 30th percentile
b. A data value in the 60th percentile
c. A data value in the 17th percentile
a. The standard score for the 30th percentile is approximately
The 30th percentile lies approximately standard deviations the mean.
b. The standard score for the 60th percentile is approximately
The 60th percentile lies approximately standard deviations the mean.
c. The standard score for the 17th percentile is approximately
The 17th percentile lies approximately standard deviations the mean.
STATUS
Question 5
Consider the distribution of the annual rainfall in 98 cities selected randomly throughout the United States. Complete parts (a) through (d) below.
a. How many peaks would you expect for the distribution?
b. Make a sketch of the distribution. Choose the correct answer below.
c. What shape would you expect for the distribution?
d. What variation would you expect in the distribution?
Question 6
Consider the distribution of the monthly sales of sunglasses over a one-year period at a store in Orlando comma FL (the distribution will look best if you start from January). Complete parts (a) through (d) below.
a. How many peaks would you expect for the distribution?
b. Make a sketch of the distribution. Choose the correct answer below.
c. What shape would you expect for the distribution?
d. What variation would you expect in the distribution?
Question 7
Exam results for 100 students are given below. For the given exam grades, briefly describe the shape and variation of the distribution.
median=85, mean=70, low score=27, high score=91
median=96, mean=90, low score=24, high score=98
Question 8
The histogram to the right shows the times between eruptions of a geyser for a sample of 300 eruptions (which means 299 times between eruptions). Over the histogram, draw a smooth curve that captures its general features. Then classify the distribution according to its number of peaks and its symmetry or skewness.
Chose the correct answer below.
