1) Suppose that 2% of all cell phone connections by a certain provider are dropped. Find the probability that in a random sample of 1, 500 calls at most 40 will be dropped. First verify that the sample is suf?ciently large to use the normal distribution.

2. Let x be a random variable that represents the length of time a student studies before an exam. It was found that x has approximately normal distribution with mean µ = 6.8 hours and standard deviation σ = 2.1 hours.

(a) What is the probability that a randomly selected student studies for at least 4 hours?

(b) Suppose 40 students are selected at random. What is the probability that the mean time ¯ x that these students studying for the exam is more than 7 hours?

3. In 2005, the distribution of the score in the math portion of the SAT test was approximately normal with a mean µ520 and a standard deviation σ = 115.

(a) What percentage of students scored more than 720 in the math portion of the SAT test in 2005?

(b) Suppose that sample of 64 students that took the SAT in 2005 is randomly selected. What is the probability that the average score ¯ x in the math portion of the SAT for these 64 students is between 491 and 549?