Exam 6: Normal Probability Distributions

Construct a normal probability plot of the given data. Use your plot to determine whether the data come from a normally distributed population -The data below represents the amount of television watched per week (in hours)for 40 randomly selected teenagers. 13 4 17 14 9 6 7 5 14 12 20 16 0 15 10 6 5 3 13 14 15 5 3 5 8 11 12 13 14 7 4 6 9 13 3 14 24 15 17 20

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. -With n = 18 and p = 0.30, estimate P(6).

Solve the problem. -For a standard normal distribution, find the percentage of data that are more than 2 standard deviations below the mean or more than 3 standard deviations above the mean.

Solve the problem. -A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is greater than 78.

Solve the problem. -A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 7.7 hours.

Provide an appropriate response. -Define a density curve and describe the two properties that it must satisfy. Show a density curve for a uniform distribution. Make sure that your graph satisfies both properties.

An airline experiences a no-show rate of 6%. What is the maximum number of reservations that it could accept for a flight with a capacity of 160, if it wants the probability of accommodating all reservation holders to be at least 95%?

List the different possible samples, and find the mean of each of them -The number of books sold over the course of the four-day book fair were 139, 199, 241, and 61. Assume that samples of size 2 are randomly selected with replacement from this population of four values.

Provide an appropriate response. -Explain why a continuity correction factor is necessary when approximating the binomial distribution by the normal distribution. Refer to the terms "discrete" and continuous", and draw a diagram to support your answer.

Provide an appropriate response. -SAT verbal scores are normally distributed with a mean of 430 and a standard deviation of 120 (based on the data from the College Board ATP). If a sample of 15 students is selected randomly, find the probability that the sample mean is above 500. Does the Central Limit theorem apply for this problem?

Provide an appropriate response. -According to data from the American Medical Association, 10% of us are left-handed. Suppose groups of 500 people are randomly selected. Find the probability that at least 80 are left-handed. Describe the characteristics of this problem which help you to recognize that the problem is about a binomial distribution which you are to solve by estimating with the normal distribution. (Assume that you would not use a computer, a table, or the binomial probability formula.)

Use the continuity correction and describe the region of the normal curve that corresponds to the indicated binomial probability. -The probability of at least 49 boys

Solve the problem. -For a standard normal distribution, find the percentage of data that are more than 1 standard deviation away from the mean.

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. -A product is manufactured in batches of 120 and the overall rate of defects is 5%. Estimate the probability that a randomly selected batch contains more than 6 defects.

Provide an appropriate response. -Complete the following table for a distribution in which $\mu = 16$ It might be helpful to make a diagram to help you determine the continuity factor for each entry. Find the probability that The continuity correction factor is: x is at least 12 xis at most 12 x is more than 12 x is less than 12

Assume that X has a normal distribution, and find the indicated probability. -The mean is $\mu = 22.0$ and the standard deviation is $\sigma = 2.4$ . Find the probability that $\mathrm { X }$ is between $19.7$ and $25.3$ .

Solve the problem. -Suppose that you wish to find $\mathrm { P } ( - 2 < \mathrm { x } < 2 )$ for a continuous uniform distribution having a minimum of $- 3$ and a maximum of 3 . If you incorrectly assume that the distribution is normal instead of uniform, will your answer be too big, too small, or will you still obtain the correct answer? Explain your thinking.

If Z is a standard normal variable, find the probability -The probability that Z is less than 1.13

The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?

If Z is a standard normal variable, find the probability -P(Z < 0.97)