Solve the following with the corresponding formulas where they apply.

1. Suppose that the number of defects in the production of electronic equipment follows an approximately normal distribution with N (20.5). This is with a mean of 20 defects and a standard deviation of 5. Use the normal distribution to determine the probability that the defects found in production are greater than or equal to 25.

2. In a clothing store, customers return 30% of the units purchased. Use the binomial distribution (see below) to determine the probability that in the next 9 sales: to.

a. Items of clothing are not returned b. 3 pieces of clothing are returned c. Less than 3 pieces are returned

3. It is intended to test the hypothesis that the average annual mortgage expense for houses purchased in Puerto Rico is $14,000. After conducting a survey with 60 families with a home, it was found that the average of the sample was $16,000 and the standard deviation of the sample was $2,000. If you want to get a 95% confidence level on the test, determine the z value.

4. Daily sales average $1,125 with a standard deviation of $100. Determine the probability that sales in the next few days will be greater than $1,125.

5. We have the number of people who attend a conference with the value N (150, 20). Determine the probability that attendance is less than 180.