Chapter 6: Q. 6.88 (page 276)
State the empirical rule as specialized to variables.
The percentage that is within one standard deviation of the mean is roughly .
The percentage within two standard deviations of the mean is per cent.
Around per cent are within three standard deviations of the mean.
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According to Table II, the area under the standard normal curve that lies to the left of is . Without further consulting Table II, determine the area under the standard normal curve that lies to the left of . Explain your reasoning.
Obtain the z-score that has an area to its left under the standard normal curve.
Elephant Pregnancies. G. Wintemeyer et al. studied demographic data on African elephants living in Kenya in the article "Comparative Demography of an At-risk African Elephant Population (PLOS ONE, Vol. 8. No. 1). Based on this study, we will assume that the time between pregnancies of the African elephant in Kenya, for elephants that have more than one calf, is normally distributed with mean of 4.01 years and a standard deviation of 0.94 years. Determine the percentage of such times that are
a. less than 2 years.
b. between 3 and 5 years.
College-Math Success. Researchers S. Lesik and M. Mitchell explore the difficulty of predicting success in college-level mathematics in the article "The Investigation of Multiple Paths to Success in College-Level Mathematics" (fraternal of Applied Reacuwh in Hreher Eiturarion, Vol. 5. Issue 1. pP, 48-57). One of the variables explored as an indicator of success was the length of time since a college freshman has taken a mathematics course. The article reports that the mean length of time is 0.18 years with a standard deviation of 0.624 years. For college freshmen, let x represent the time, in years, since taking a math course.
A . What percentage of times are at least 0 years?
b. Assuming that x is approximately normally distributed, tose normal curve areas to determine the approximate percentage of times that are at least 0 years.
c. Based on your results from parts (a) and (b), do you think that the length of time since taking a math course for college freshmen is approximately a normally distributed variable? Explain your answer.
A variable is normally distributed with a mean and standard deviation. Find the percentage of all possible values of the variable that
a. lie between and .
b. are at least .
c. are at most .
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