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Math 1530 Chapter 5 Review Problems
- A banks loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a s.d. = 20.
A. If an applicant is randomly selected, find the probability of a rating that is between 180 and 225.
B. If an applicant is randomly selected, find the probability of a rating that is below 215.
C. If an applicant is randomly selected, find the probability of a rating above 240.
D. Find P 70 , i.e. the score which separates the lower 70% from the top 30%.
E. If a group of 36 applicants is randomly selected, find the probability of a mean rating between 202 and 212.
F. If a group of 100 applicants is randomly selected, find the probability of a mean rating greater than 198.
- An educational testing corporation has designed a standardized test of mechanical aptitude. Scores on this test are normally distributed with a mean = 75 and s.d. = 15.
A. If a subject is randomly selected and tested, find the probability that his score will be between 85 and 100.
B. If a subject is randomly selected and tested, find the probability that his score will be above 100.
C. If a subject is randomly selected and tested, find the probability that his score will be below 85.
D. If a subject is randomly selected and tested, find the probability that his score will be between 69 and 81.
E. Find P 33 , i.e. the score which separates the lower 33% from the upper 67%.
F. Find Q 3.
G. If a group of 49 students is randomly selected and tested, find the probability that the mean score will be between 80 and 95.
H. If a group of 81 students is randomly selected and tested, find the probability that the mean score of this group will be below 72.
- Assume X has a normal distribution, with mean = 40 and s.d. = 12. Find P(X < 46).
- Assume that weights of quarters are normally distributed with mean = 5.67 g. and s.d. = 0. g. A vending machine will only accept coins weighing between 5.48 g. and 5.82 g. What percentage of legal quarters will be rejected?
- IQ scores are normally distributed with mean = 100 and s.d. = 15. In a random sample of 9,000 people, approx how many would have IQ’s between 85 and 120?
- A final exam in Math 1530 has a mean = 73 with s.d. = 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is less than 76.
