7.34 Suppose that for a given computer salesperson, the probability distribution of x = the number of systems sold in 1 month is given by the following table: 1 2 3 4 5 6 8 p(x) .05 .10 .12 .30 .30 .11 .01 .01 a. Find the mean value of x (the mean number of systems sold). b. Find the variance and standard deviation of x. How would you interpret these values? c. What is the probability that the number of systems sold is within 1 standard deviation of its mean value? d. What is the probability that the number of systems sold is more than 2 standard deviations from the mean? (Hint: See Example 7.13.)

A market research company is interested in the home owership rates across Melbourne suburbs. They survey 253 households in the suburb of Carlton where the true probability of being a home owner for a given household is 0.782. Assume that the home ownership status of each households is independent of others. 1. What is the distribution of X? 2. What is the variance of X? 3. What is the probability that X is greater than 200 ? 4. What is the probability that X is less than or equal to 200?

A population has a mean of 300 and a standard deviation of 40. Suppose a simple random sample of size 100 is selected and Z is used to estimate . Use z table. a. What is the probability that the sample mean will be within +8 of the population mean (to 4 decimals)? b. What is the probability that the sample mean will be within +10 of the population mean (to 4 decimals)?

5. Question from 8.3: Variance and Standard Deviation Find the variance of the probability distribution for the histogram shown. 0.3 0.2 0.1 1 2 3 4 5 X

4. Review the variance function for specific distributions. For Bernoulli, Poisson, Gamma, and Inverse Gaussian, what does the variance function say about our ability to predict the range of possible values? (This may be a little bit challenging; give it your best guess.)

6.36. Suppose that for a given computer salesperson, the probability distribution of x = the number of systems sold in 1 week is given by the following table: 1 2 3 4 7 8 p(z) 0.05 0.10 0.12 0.30 0.30 0.11 0.01 0.01 a. Find the mean value of æ (the mean number of systems sold). b. Find the variance and standard deviation of æ. How would you interpret these values? c. What is the probability that the number of systems sold is within 1 standard deviation of its mean value? d. What is the probability that the number of systems sold is more than 2 standard deviations from the mean?

6.2 The Standard Normal Distribution Table: Z-score and Probability A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 164.7 cm and a standard deviation of 2.5 cm. Find the probability that the length of a randomly selected steel rod is greater than 167.7 cm. Probability -

The following table gives the frequency distribution of the number of errors committed by a college baseball team in all of the 47 games that it played during the 2011-12 season.     Number of Errors Number of Games 0 11 1 16 2 9 3 7 4 3 5 1     Find the mean, variance, and standard deviation. (Hint: The classes in this example are single valued. These values of classes will be used as values of m in the formulas for the mean, variance, and standard deviation.)Round your answers to two decimal places. Mean = Enter you answer; Mean errors Variance = Enter you answer; Variance Standard deviation = Enter you answer; Standard deviation errors

4. 3. 20 2. The following data show the probability distribution of the number os Android Cellular Phones sold daily in the Inday CP Shop during the past several months: Number of Android Phones (X) Probability P(X) 0. 0.10 0.20 0.45 0.15 0.05 0.05 a. Find the mean and variance of the prebability distribution. b. Interpret the mean and the variance of the problem.

1. The probability that a planted radish seed germinates is 0.80. A gardener plants nine seeds. Let X denote the number of radish seeds that successfully germinate? What is the variance and standard deviation of X? State your answer in 2 decimal place value