The COVID-19 infection rate in Philadelphia has decreased recently. Assume that the rate of testing positive is 5% in the first week of March 2021.Out of 7 randomly selected residents of Philadelphia, random variable X= number of infected out of 7.What is

• The probability that at most 2 are infected?
• The probability that between 3 and 5 (inclusive) are infected?
• What are the mean and variance of X?

In South Jersey, the rate of testing positive is 3.65%, lower than Philadelphia.Out of 25 south NJ residents, what is the probability that between 2 and 5 (inclusive) will be testing positive? (20 points)

WangCo supplies an under-hood, emissions control air pump to the automotive industry.The company's current air pump lasts an average of 63,000 miles, with a standard deviation of 10,000 miles.Assume that the number of miles a pump operates before becoming ineffective to be normally distributed. If a pump fails before the vehicle in which it is installed has covered 50,000 miles, federal emissions regulations require that it be replaced at no cost to the vehicle owner.

(a)For the current pump design, what percentage of the company's pumps will have to be replaced at no charge to the consumer?

(b)What percentage of the company's pumps will fail between 45,000 and 55,000 miles?

(c) For what number of miles does the probability become 85% that a randomly selected pump will no longer be effective?

12:37 PM Mon Mar 29 5? 35% I B sakairutgersvedu 7 i RUTGERS Sakai