Question

1. It is speculated that the proportion p of students who paid more than $5000 tuition this year is p = .58. A sample of 680 students was collected. Assuming that this speculation is correct, what is the prob- ability that more than 400 would have paid more than $5000 in tuition (i.e. sample mean would be more than 400/680)? (Use CLT.)

2. A gross estimate of a fisherman is that that 65 percent of the salmon in a river exceed thirty pounds in weight. A fisherman catches 480 salmon. Assuming his/her gross estimate, what is the probability that less than 300 would be above thirty pounds (i.e. sample mean would be less than 300/480)? (Use CLT.)

3. It is assumed that proportion of tomatoes above 225 grams is p = .72. What is the probability that a sample of 200 tomatoes would have less than 150 tomatoes above 225 grams (i.e. sample mean would be less than 150/200)? (Use CLT.)

4. It is assumed that 52 percent of the population take less than thirty minutes to commute to work. In a sample 720, what is the probability that more than 370 commute less than thirty minutes (i.e. sample mean would be more than 370/720)? (Use CLT.)

5. It is speculated that in a rainy season, in a region, probability that it will rain at least one inch is p = .80. What is the probability that for more than 100 days it will rain more than an inch, in a season of 120 days (i.e. sample mean would be more than 100/120)? (Use CLT.)

Answer 1