Question

Scores on a test are normally distributed with a mean of 68.2 and a standard deviation of 10.4. Estimate the probability that among 75 randomly selected students, at least 20 of them score greater than 78.

Answer 1

2.78458131857796%

Explanation:

Start by standardizing the 78 by subtracting the mean then dividing by the standard deviation

(78-68.2)/10.4= 0.942307692308

I'm going to assume that you have some sort of computer program that can convert this into a probability (rather than just using a normal table).

start by converting this into a probability: 82.6982434497094%. this gives us the probability that there score is less than 78. we want the probability that their score is more than 78. to find this, take the compliment: (1-0.826982434497094)= 0.173017565502906. From here, just use a binomial distribution to solve for the probability of 20 or more students having a score greater than 78. using excel, i get 2.78458131857796%.

As a note, if you are supposed to use a normal table, the answer would be 2.87632246854082%