STAT 200 Homework Solution

1. You draw two cards from a deck, what is the probability that:
2. both of them are face cards (king, queen, or jack)?
2. you draw two cards from a deck and both of them are hearts

2. Assume adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15.

1. Find the probability that a randomly selected adult has IQ < 115
2. Find the probability that a randomly selected adult has IQ > 70
3. Find P_30, which is the IQ separating the bottom 30% from the top 70%

3. a.  When would the mean grade in a class on a final exam be considered a statistic?

b.  When would it be considered a parameter?

c.. Define bias in terms of expected value.

2.  Is it possible for a statistic to be unbiased yet very imprecise? Can it be accurate but biased?

4.a.  Why is a 99% confidence interval wider than a 95% confidence interval?

     b.  When you construct a 95% confidence interval, what are you 95% confident about?

5.My parents lived in Florida and wanted to know the probability of winning the Florida Fantasy 5 if they bought one ticket. They had to pick the five winning numbers from 1-

36. Each randomly selected number is different and order doesn’t matter. What is the Probability of their winning?

6.In a study of families with children with disabilities, group of 6 US households wererandomly selected. In the table below, the random variable x represents the number of households among 6 that had a child with a disability living there.

1. Is this a probability distribution?
2. What is the mean?
3. What is the standard deviation?

7.Ten peas are generated from parents having the green/yellow pair of genes so there is a 75% probability that an individual pea will have a green pod. Find the probability that among the 10 offspring peas, at least 9 have green pods. Is this unusual? Explain.

8.  Find the critical value

a. Z_0.02

b. Z_0.01

c. Z_0.10