Question

There are 45 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time needed to grade a randomly chosen first examination paper is a random variable with an expected value of 5 min and a standard deviation of 4 min. (Round your answers to four decimal places.) (a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins? .8243 0.8243 (b) If the sports report begins at 11:10, what is the probability that he misses part of the report if he waits until grading is done before turning on the TV? .0961 0.0961

Answer 1

To find the probability that at least 40 out of 50 students do their homework on time, we can use the binomial probability formula.

Step-by-step explanation:

To find the probability that at least 40 out of 50 students do their homework on time, we can use the binomial probability formula:

P(X ≥ k) = 1 - P(X < k)

Where X is the number of students who do their homework on time and k is the desired number of students (40). The probability of a student doing their homework on time is 0.70. Plugging in these values, we can calculate the probability:

P(X ≥ 40) = 1 - P(X < 40) = 1 - ∑ (P(X = 0) + P(X = 1) + ... + P(X = 39))

Using a binomial probability calculator or a cumulative binomial distribution table, we can find that the probability is approximately 0.9999.