1) You survey 1,000 families with 4 children

1) You survey 1,000 families with 4 children. You assume the probability of having a boy child is the same has having a girl child. How many families do you expect to have at least one boy?

2. You believe that the probability of a defective circuit is 0.025. Defects follow a binomial distribution. a. What are the expected number of defective circuits and the standard deviation of the number of defective circuits in a sample of 1,000 circuits? b. What is the probability that you find 5 defective circuits in a sample of 100 circuits?

3. On an exam, the mean grade is 85 and the standard deviation is 4. You decide to standardize the scores, transforming each score into a Z statistic. a. What is the Z statistic for a student with a grade of 90? b. What is the Z statistic for a student with a grade of 75? c. What is the probability that a student score was higher than 90? You will need a Z table to answer this question (you can find one on the Canvas page containing this assignment).

4. X ~ N(μ=4, σ2 = 2). What is the probability that X is between 3.5 and 5.0, i.e., P(3.5 < X < 5) ?