A, A fire insurance company claimed that the mean distance from a home to the nearest fire department in a suburb of Boston was at least 5.2 miles. It sets its insurance rate accordingly. Members of the community disagreed, and randomly identified 105 homes and found that their average distance to the nearest fire department was 4.5 miles. Ifmiles, does the sample show sufficient evidence to reject insurance company's claim with?

B. A fish hatchery manager wants to estimate the mean length of her 3-year-old hatchery raised trout. She wants to make a 96% confidence interval accurate to within 1/5 of a standard deviation. How large a sample does she need to take?

C.The water pollution readings at State Park Beach seem to be lower than that of the prior year. A sample of 16 readings (measured in coliform/100mL) was randomly selected from the records of this year's daily readings:

3.6, 3.8, 2.7, 3.0, 3.1, 3.4, 4.8, 3.3, 2.4, 3.6, 4.3, 3.1, 3.7, 3.4, 3.5, 3.9

a. Does this ample provide sufficient evidence to conclude that the mean of this year's pollution readings is significantly lower than that of last year's mean of 3.59 at 0.01 level?

b. Find a 90% confidence interval for population.

D, a. An insurance company states that 85% of its claims are settled with 3 weeks. Ms. Jhon Gomes led a consumer group to challenge this statement. 150 past claims were checked, 119 of them are settled in 3 weeks. Does this show that less than 85% of the claims are settled in 3 weeks? Use=0.06

b. Find the 92% confidence interval for the proportion (percentage) of claims that can be settled with 3 weeks.

E, It is claimed that Pfizer vaccine is 98% effective upon taking two shots, suppose that all 2500 CVD members are vaccinated of taking two shots of Pfizer vaccine, is it very likely that more than 100 will be infected? To answer this question, please calculate the probability that more than 100 be infected.

F, the 95% confidence interval foris:

.

PX, - 1.96 Sux + 1.96-) = 95%. a. Please verify that: P (X, - 1.85- Susx, + 2.1-) = 95% is also true. b. Regarding the confidence interval for A, can you explain why x - 1.96 -Sux, + 1.96- is better than x, - 1.85- Sux, + 2.1- vn