Find solutions

9. There is a 0.8 probability that the temperature will be below freezing on

any winter's day in Toronto. Given that the temperature is below freezing

my car fails to start 15 percent of the time. Given that the temperature is

above freezing my car fails to start 5 percent of the time. Given that my

car starts, what is the probability that the temperature is below freezing?

10. If a baseball player is hitting .250 (i.e., if averages one hit per four times

at bat), how many times will he have to come up to bat to have a 90%

chance of getting a hit? Hint: Ask yourself what the probability is of not

getting a hit in n times at bat. Then take advantage of the fact that the

event 'getting at least one hit in n times at bat' is the complementary event

to the event of 'not getting a hit in n times at bat'.

11. A particular automatic sprinkler system for high-rise apartment buildings, office buildings, and hotels has two different types of activation devices

on each sprinkler head. One type has a reliability of .91 (i.e., the probability that it will activate the sprinkler when it should is .91). The other

type, which operates independently of the first type, has a reliability of .87.

Suppose a serious fire starts near a particular sprinkler head.

a) What is the probability that the sprinkler head will be activated?

b) What is the probability that the sprinkler head will not be activated?

c) What is the probability that both activation devices will work properly?

d) What is the probability that only the device with reliability .91 will

work properly

2. Suppose that Y, and Yz are continuous random variables with the joint probability density function (joint pdf) f(1. Y2) = ky; (y, + 2):0 58, a sample of n = 100 observations possessed mean i = 5?.2 and standard deviation 5 = 5.2. Find and interpret the p-value for this test. The p-value for this test is D. (Round to three decimal places as needed.) Interpret the result. Select the correct choice below and ll in the answer box to complete your choice. (Round to three decimal places as needed.) 0 A. The probability (assuming that H0 is true) of observing a value of the test statistic that is equal to the null hypothesis is D. O B. The probability (assuming that H0 is true) of observing a value of the test statistic that is at least as contradictory to the null hypothesis is El. 0 C. The probability (assuming that Hat is true) of observing a value of the test statistic that is at most as contradictory to the null hypothesis is D. In a test of the hypothesis Ho: ul = 53 versus Ha : p > 53, a sample of n = 100 observations possessed mean x = 52.3 and standard deviation s = 4.3. Find and interpret the p-value for this test. The p-value for this test is 0.948 . (Round to three decimal places as needed.) Interpret the result. Select the correct choice below and fill in the answer box to complete your choice. (Round to three decimal places as needed.) O A. The probability (assuming that Ho is true) of observing a value of the test statistic that is at least as contradictory to the null hypothesis is O B. The probability (assuming that He is true) of observing a value of the test statistic that is at most as contradictory to the null hypothesis is O C. The probability (assuming that He is true) of observing a value of the test statistic that is equal to the null hypothesis isQuestion 19 3 pts If a 95% CI does not contain the value of the null hypothesis, then for the hypothesis test calculating a P-value, O if it is a Fisher's exact test, the result will be statistically significant; however, if it is a Chi- squared test, the result will not be statistically significant. O the result must be statistically significant O the result must not be statistically significant O if it is a Chi-squared test, the result will be statistically significant; however, if it is a Fisher's exact test, the result will not be statistically significant. O the result could be either statistically significant or not statistically significant