Statistics and Probability Answers

A study was conducted to determine whether there exists a relationship between the length of time (in hours) a senior high school student spends reviewing his or her lesson a week before the final examination and his or her grade in statistics and probability. Eight randomly selected senior high school students provided the following data.

x 10 12 24 20 13 13 8 22

y 80 83 94 90 85 84 80 89

Find the slope (a) and y-intercept (b) of the regression line. Interpret the results.

Predict the grade of a student who reviewed 15 hours a week before the final examination in statistics and probability.

Compute the Pearson’s r. Interpret the results.

Does the length of time (in hours) a senior high school student spends reviewing his or her lesson a week before final examination have significant effect to his or her grade in statistics and probability? Used 0.05 level of significance.

DEADLINE : 05/12/2022 11 : 00 PM

A study was conducted to determine whether there exists a relationship between the length of time (in hours) a senior high school student spends reviewing his or her lesson a week before the final examination and his or her grade in statistics and probability. Eight randomly selected senior high school students provided the following data.

x 10 12 24 20 13 13 8 22

y 80 83 94 90 85 84 80 89

Find the slope (a) and y-intercept (b) of the regression line. Interpret the results.

Predict the grade of a student who reviewed 15 hours a week before the final examination in statistics and probability.

Compute the Pearson’s r. Interpret the results.

Does the length of time (in hours) a senior high school student spends reviewing his or her lesson a week before final examination have significant effect to his or her grade in statistics and probability? Used 0.05 level of significance.

The number of content changes to a Web site follows a Poisson distribution with a mean of

0.25 per day.

a. What is the probability of two or more changes in a day?

b. What is the probability of no content changes in five days?

c. What is the probability of two or fewer changes in five days?

If a publisher of nontechnical books takes great pains to ensure that its books are free of

typographical errors, so that the probability of any given page containing at least one such error is 0.005

and errors are independent from page to page,

a. What is the probability that one of its 400-page novels will contain exactly one page with errors?

b. What is the probability that one of its 400-page novels will contain exactly one page with errors

given that it contains at least one page with errors?

A parabolic satellite dish reflects signals to the dish’s focal point. An antenna designer analyzed signals transmitted to a satellite dish and obtained the probability density function 𝑓𝑥(𝑥) = { 𝑐 (1 − 1 /16* 𝑥*2) , 0 < 𝑥 < 2; 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 where X is the distance (in meters) from the centroid of the dish surface to a reflection point at which a signal arrives. Determine the following: a. Value of 𝑐 that makes 𝑓𝑥(𝑥) a valid probability density function. b. 𝑃(0.1 < 𝑋 < 0.4). c. 𝐸(𝑋) and 𝑉𝑎𝑟(𝑋)

Suppose that 2 batteries are randomly chosen without replacement from the following groupof 9 batteries: 3 new, 4 used (working), 2 defective. Let X denote the number of new batteries chosen. Let Y denote the number of used batteries chosen. a. Find the joint probability distribution, 𝑃(𝑋 = 𝑥, 𝑌 = 𝑦). b. Find 𝐸[𝑋].