Chapter 7 Test: Continuous Probability Distributions.

Chapter 7 Test: Continuous Probability Distributions.

For a random variable X that is distributed normally with a mean of 5 and a variance of 4, the z-score of x = 4.2 is? (1 k/A)

The lifetimes of a certain brand of photographic light are normally distributed with a mean of 210 hours and a standard deviation of 50 hours.

What is the probability that a particular light will last more than 250 hours? (2 k/A)

What percent of lights will need to be replaced within 235 hours? (2 K/A)

Out of 2000 lights, how many will have a lifetime between 200 and 350 hours. (2 K/A)

As the official data collector for the school track and field team, Jay knows that the amount of time high school runners can complete the 400 m race is normally distributed with a mean of 40 seconds with a standard deviation of 0.5 seconds. So when Richard told him that he could complete the 400 m race in 34 seconds, Jay refused to believe him. Explain with the help of z scores why Jay does not believe Richard. (4 C)

In a recent article the CBC reported that a recent survey reviled that 55% support the new law. And that this is accurate within 3% 19 times out of 20. Explain what this means. (4C)

Sam and Mary conducted a survey of 50 male students and 50 female asking them how many hours per week they spend studying math per week. The results are the following for males the mean was 4.5 hours with a standard deviation of 0.3 hours, for females the mean was 5.1 hours with a standard deviation of 0.2 hours.

Calculate the 95% confidence intervals for male students (3 k /A)

Calculate the 95% confidence interval for female students (3 k/A)

Based on the results from parts a) and b) do females students study more than males? (2 k/A)

The heights of the students at Clarkson Secondary School is normally distributed with a mean of 158 cm and standard deviation of 10 cm. In what RANGE of heights would you have to be in the middle 80% (meaning 10% above, 10 % below). (4T)