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) ?
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