1. By current estimates, 20% of home-based computers have access to on-line services. Suppose that 25 people with home-based computers were randomly and independently sampled. Using this histogram, estimate the probability that at least 3 of the 25 sampled currently have access to on-line services.
2. A local bakery has determined a probability distribution for the number of cheesecakes that they sell in a given day. The distribution is as follows:
Find the number of cheesecakes that this local bakery expects to sell in a day.
3. A recent article in the paper claims that only 1/4 of American adults pronounce the word “realtor” correctly. Suppose that 20 adults are randomly and independently sampled. Assume that the paper’s claim is accurate.
(a) Find the probability that none of those sampled pronounce the word “realtor” correctly.
(b) Find the probability that at least one of those sampled pronounce the word “realtor” correctly.
(c) Find the probability that exactly one of those sampled pronounce the word “realtor” correctly.
4. A physical fitness association is including the mile run in its secondary-school fitness test for boys. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 450 seconds and a standard deviation of 50 seconds. The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition from the fitness association?
5. The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.
6. The amount of soda that a dispensing machine pours into a 12 ounce can follows a normal distribution with a mean of 12.03 ounces and a standard deviation of .02 ounces. What proportion of the soda cans filled by this machine contain more than the advertised 12 ounces of soda?
7. Transportation officials tell us that 60% of the population wear a seatbelt while driving. A random sample of 1000 drivers has been taken. Let x be the number of drivers in the sample who were wearing a seatbelt, and note that x is a binomial variable for which n = 1000 and p = .60.
(a) What is the mean (expected value) of x ?
(b) What is the standard deviation of x ?
(c) The distribution of x is approximately normal. Find the approximate probability that more than half of the 1000 sampled were wearing their seatbelts.