# Mathematics Questions: frequency distribution

Subject: Mathematics    / General Mathematics
Question
Dogs     Households
0     1269
1     424
2     162
3     40
4     27
5     16

Problem # 6. A frequency distribution is shown below. Complete parts 9a) through (e). The number of dogs per household in a small town.

(a) Use the frequency distribution to construct a probability distribution. (Round to the nearest thousandth as needed).

(b). Find the mean of the probability distribution. (round to the nearest tenth as needed)

(c) Find the variance of the probability distribution (round to the nearest tenth as needed)

(d) Find the standard deviation of the probability distribution (round to the nearest tenth as needed)

(e) Interpret the results in the context of the real life situation.

Problem # 8. Use technology to (a) construct and graph a probability distribution and (b) describe its shape. The number of computers per household in a small town
Computers     0     1     2     3
Households     303     282     100     15

(a) construct the probability distribution by completing the table below.

Problem # 9. For a random variable x, a new random variable y can be created by applying a linear transformation y= a + bx, where a and b are constants. If the random variable x has mean and standard deviation ox, then the mean, variance and standard deviation. The mean annual salary for employees at a company is \$35,000. At the end of the year, each employee receives a \$5000 bonus and a 9% raise (based on salary). What is the new mean annual salary (including the bonus and raise) for the employees? The means annual salary is \$—

Problem #12. Find the mean, variance and standard deviation of the binomial distribution with the given values of n and p. n = 70, p = 0.7 The mean is —(round to the nearest tenth as needed) The variance is —(round to the nearest tenth as needed) The standard deviation is —(round to the nearest tenth as needed)

Problem#13. Thirty five percent of households say they would feel secure if they had \$50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had \$50,000 in savings. Find the probability that the number that say they would feel secure is (a) exactly five, (b) more than five and (c) at most five.

(a) find the probability that the number that say they would feel secure is exactly five P(5)= (round to three decimal places as needed)

(b) find the probability that the number that say they would secure is more than five P(x>5)= (round to three decimal places as needed)

(c) find the probability that the number that say they would secure is at most five. P (x<5)= (round to three decimal places as needed)

Problem # 14. 22% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the number of college students who say they use credit cards because of the rewards programs (a) exactly two, (b) more than two and (c) between two and five inclusive. If convenient use technology to find the probabilities.

(a) P(2) = –(round to the nearest thousandth as needed)

(b) P(x > 2) = –(round to the nearest thousandth as needed)

(c) P (2 < x < 5)=—(round to the nearest thousandth as needed)

Problem # 26. The SAT is an exam used by colleges and universities to evaluate undergraduate applicants. The test scores are normally distributed. In a recent year the mean test score was 1505 and the standard deviation was 314. The test scores of four students selected at random are 1944, 1333, 2265, and 1380. Complete parts (a) through (c)below.

(a) Without converting to z-score match the values with the letters A,B,C, and D on the given graph of the standard normal distribution . graph is a hill with the letters in the middle. A= B= C= D=

(b) Find the z-score that corresponds to each value and check your answers to part (a). Za= Zb=

Zc= and Zd=

round to two decimal places as needed)

(c) Determine whether any of the values are unusual. Select the correct answer below and if necessary fill in the answer boxes within your choice. A. The unusual values is/are—. The very unusual value(s) is/are—(use a comma to separate answers as needed) B. The very unusual value(s) is/are—. The unusual values are all very unusual. (use a comma to separate answers as needed)C. The unusual value(s) is/are—. There are no very unusual values. (use a comma to separate answers as needed. D. There are no unusual or vey unusual values.

Problem # 29. The mean incubation time a type of fertilized egg kept at 100.4F is 19 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 1 day.

(a) The probability that a randomly selected fertilized egg hatches in less than 17 days is—

(b) The probability that a randomly selected fertilized egg hatches between 18 and 19 days is –(round all of these to four decimal places as needed)

(c) The probability that a randomly selected fertilized egg takes over 21 days to hatch is —

Problem # 30. The total cholesterol levels of a sample of men aged 35-44 are normally distributed with a mean of 212 milligrams per deciliter and a standard deviation of 38.2 milligrams per deciliter.

(a) What percent of the men have a total cholesterol level less than 239 milligrams per deciliter of blood?

(b) If 254 men in 35-44 age group are randomly selected about how many would you expect to have a total cholesterol level greater than 252 milligrams per deciliter of blood?

(a) The percent of the men that have a total cholesterol level less than 239 milligrams per deciliter of blood is—%.

(b) Of the 254 men selected,— would be expected to have a total cholesterol level greater than 252 milligrams per deciliter of blood. (round to the nearest integer as needed)

Problem # 37. Find the probability and interpret the results. If convenient use technology to find the probability. The population mean annual salary for environmental compliance specialists is about \$62,000. A random sample of 40 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than \$58,500. Assume mean is \$58,500.

The probability that the mean salary of the sample is less than \$58,500 is —. Interpret the results. Choose the correct answer below.

A. Only 0.01% of samples of 40 specialists will have a mean salary less than \$58,500. B. About 1%of samples of 40 specialists will have a mean salary less than \$58,500. This is an extremely unusual event. C. Only 1% of samples of 40 specialists will have a mean salary less than \$58,500. This is an extremely unusual event. D. About 0.01% of samples of 40 specialists will have a mean salary less than \$58,500. This is not an unusual event.