Probability Question

5. Determine whether the data in Table 1 is a probability distribution. If not, identify the requirement that is not satisfied.

Table 1

x P(x)

0 0.1296

1 0.3456

2 0.3456

3 0.1536

4 0.0256

12. The number of books sold over the course of the four-day book fair were 194, 197, 247, and 76. Assume that samples of size 2 are randomly selected with replacement from this population of four values. List the different possible samples, and find the mean of each of them.

18. Define margin of error. Explain the relation between the confidence interval and the margin of error. Suppose a confidence interval is 9.65 < μ < 11.35. Redefine the confidence interval into a format using the margin of error and the point estimate of the population mean.

24. Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the original claim.

A cereal company claims that the mean weight of the cereal in its packets is 14 oz. The weights (in ounces) of the cereal in a random sample of 8 of its cereal packets are listed below. Test the claim at the 0.01 significance level.

25. Use the given values of n = 1205 and p = 0.98 to find the maximum value that is significantly low, μ – 2σ, and the minimum value that is significantly high, μ + 2σ. Round your answer to the nearest hundredth unless otherwise noted.