Dr Nick
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Question description
Answer all questions. Please show all necessary work
Consider the following probability function P(x) = x / 15 for x =1, 2, 3, 4, or 5.
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x |
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P(x) |
3. Find and .
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xP(x) |
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X2P(x) |
4. Find the mean of the probability distribution.
5. Find the variance of the probability distribution.
6. A carton containing 75 towels is inspected. Each towel is rated “first quality” or “irregular”. After all 100 towels are inspected, the number of irregulars is reported as a random variable. Explain why x is a binomial variable
Four cards are selected, one at a time, from a standard deck of 52 cards. Let x represent the number of aces drawn in the set of 4 cards.
7. If this experiment is completed without replacement, explain why x is not a binomial random variable.
8. Find the mean and standard deviation of x = number of right-handed students in a classroom of 30 students. Assume that 10% of the population is left-handed.
9. The probability of success on a single trial of a binomial experiment is known to be 0.40. The random variable x, number of successes, has a mean value of 80. Find the number of trials involved in this experiment and the standard deviation of x.
A doctor knows from experience that 20% of the patients to whom he gives a high blood pressure drug will have undesirable side effects. Assume the doctor gives that drug to ten of his patients.
10. Find the probability that among the ten patients to whom he gives the drug, at most two will have undesirable side effects.
11. Find the probability that among the ten patients to whom he gives the drug, at least three will have undesirable side effects.
12. Find the area under the standard normal curve to the left of z = 1.53.
13. Find the area under the standard normal curve between z = -1.42 and z =1.35.
14. The random variable z is the standard normal score. Find z as shown in the diagram below given that the area of the shaded region is 0.4927.
Suppose that daycare costs are normally distributed with a mean equal to $12,000 a year and a standard deviation equal to $3,000.
15. What percentage of daycare centers will cost between $9,000 and $13,000?
16. Find the normal approximation for the binomial probability P(x = 8), where n = 15 and p = 0.3.
Consider the set of numbers {4, 8, 10, 12}.
17. Make a list of all possible samples of size 2 that could be drawn with replacement from
the above set of numbers.
18. Construct the sampling distribution of sample means for the samples in question 17.
Suppose the annual consumption of chicken mean is 20.84 pounds per person, and that the standard deviation for the consumption of chicken per person is 9.193 pounds. The mean weight of chicken consumed for a sample of 200 randomly selected people is one value of many that form the sampling distribution of sample means.
19. What is the probability that this sample mean will be between 68 and 82?
Assume that the population of heights of male college students is normally distributed with mean μ of 68 inches and standard deviation σ of 3.75 inches. A random sample of 16 heights is obtained.
20. Find the mean and standard error of the distribution.