1. Suppose a density curve has an area of 0.361 to the left of 12 and an area of 0.428 to the right of 14. What is the size of the area between 12 and 14? Explain your answer.

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2. Determine the -scores that mark the 15th percentile and the upper 0.4% of the standard normal distribution.

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3. The weekly television viewing time of children aged 2 - 11 years is normally distributed with a mean of 24.50 hours and a standard deviation of 6.23 hours.

a) What percentage of children watch more than 34 hours of television per week?

b) What percentage of children watch between 10 and 20 hours of television per week?

c) Determine the 25th percentile of the distribution of weekly television viewing time for children aged 2 - 11 years.

d) Determine the number of hours of television watched weekly by children aged 2 - 11 years that marks the upper 5% of this distribution.

e) There is some evidence that children who watch more than 14 hours of television weekly may have attention problems as young teens. What percentage of the children in this distribution may have attention problems as young teens?

f) There is some evidence that children who watch more than 14 hours of television weekly may have attention problems as young teens. Compute the probability that every child in a random sample of 5 children aged 2 - 11 years may have attention problems as young teens.

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4. Suppose we are studying an extremely right-skewed population with mean = 10 and standard deviation = 5. What are the parameters of the sampling distribution of the same mean for samples of size n = 50?

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5. What is the shape of the sampling distribution of the sample mean in question 4? Explain.

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6.Do the parameters of the sampling distribution of the sample mean change for different types of population (e.g., skewed vs. symmetric) and different sample sizes? Explain.

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7.Suppose we collect a sample of size n = 10 from some population. Under what condition is the sampling distribution of the sample mean normally distributed?

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8. Letdenote the amount of time a randomly selected customer spends on hold with some insurance company. Suppose X follows a distribution with a mean of 8 hours and a variance of 16 hours. The population density curve for X is shown below.