**Problem 3:** The grade point averages of a large population of college students is approximately normally distributed with a mean of 2.4 and a standard deviation of 0.8. What fraction of the students will possess a grade point average in excess of 3.0?**Problem 4:** Refer to problem 3. If students possessing a grade point average less than 1.9 are dropped from the college, what percentage of the students will be dropped?

Let X be the grade point average of large population of college students.Given, X is approximately…

Answered: 3) The grade point averages of a large…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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16.
4. The specification of the melting point of an alloy is 1200 degrees Celsius. If the melting point differs from this by more than 20 degrees, the composition of the alloy will have to be changed. Assume the melting point is normally distributed with standard deviation 35 degrees. A sample of 25 alloys were obtained and the average melting point were 1224 degrees. By using a = 0.01, determine whether the composition of the alloy will have to be changed? JTM
7. A distribution with u = 35 and s = 8 is being standardized so that the new mean and standard deviation will be u = 50 and s = 10. In the new, standardized distribution your score is X = 45. What was your score in the %3D original distribution?
13)Many graduate schools require applicants to take the GRE for admission. The mean GRE score worldwide is 149.7 with a standard deviation of 8.2. The recommended overall GRE score for admission at UC Berkeley is 153 Q) If an applicant were to obtain a score of 123, how many standard deviations away is this score from the mean?
Suppose that the City of Chicago is interested in potential revenues if they introduce a tolling station near O'Hare. Further suppose that the average time between cars is only 3.0 seconds; what is the average value of the distribution?
30. The distribution of weights for 12-month-old baby girls in the US is ap- proximately normal with mean u = 21 pounds and standard deviation o = 2.2 pounds. a) If a 12-month-old girl weighs 23.2 pounds, approximately what weight percentile is she in? b) If a 12-month-old girl is in the 16th percentile in weight, estimate her weight. c) Estimate the weight of a 12-month-old girl who is in the 25th percentile by weight. d) Estimate the weight of a 12-month-old girl who is in the 75th percentile by weight.
15. A sample has a mean M = 75. In the sample, a score of X = 95 corresponds to z = 2.5 What is the standard deviation for the sample?
if a variable has a distribution that is bell-shaped with mean 21 and standard deviation 7, then according to the Empirical Rule, what percent of the data will lie between 0 and 42?
4. A normally distributed set of 1,010 values has a mean of 103 and a standard deviation of 12. Which is closest to the number of values expected to be below 88?
6. A comparison of life expectancy in random samples of 40 less-developed countries and 31 industrialized countries reveals the following (fictional) data. The standard deviations are significantly different from one another. Is there a significant difference in mean life expectancy between countries with these two levels of economic development? X=life expectancy of the resident at birth. Less-Developed Countries Mean=66.1 years N=40 Standard error of the difference between means=.60 Industrialized Countries Mean=76.7 years N=31
4. The specification of the melting point of an alloy is 1200 degrees Celsius. If the melting point differs from this by more than 20 degrees, the composition of the alloy will have to be changed. Assume the melting point is normally distributed with standard deviation 35 degrees. A sample of 25 alloys were obtained and the average melting point were 1224 degrees. By using a = 0.01, determine whether the composition of the alloy will have to be changed? UTM UTM
A normal population has a mean μ = 31 and standard deviation = 8. What proportion of the population is less than 29?

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