Let X represent the results of the toss of a fair die. Find the following probabilities.
a. P(X =1)
b. P(X=6)
Let X represent the mean of the toss of two fair dice. Use the probabilities listed in Table 9.2 to determine the following probabilities.
a. P(X=1)
b. P(X=6)
An experimental consists of tossing five balanced dice. Find the following probabilities. (Determine the exact probabilities as we did in Tables 9.1 and 9.2 for tow dice.)
a. P(X=1)
b. P(X=6)
Refer to Exercises 9.1 to 9.3. What do the probabilities tell you about the variances of X and X bar?
A normally distributed population has a mean of 40 and a standard deviation of 12. What does the central limit theorem say about the sampling distribution of the mean if samples of size 100 are drawn from this population?
In a random sample of 500 observations, we found the proportion of successes to be 48% Estimate with 95% confidence the population proportion of successes.
Repeat part (a) with n = 200
Repeat part (a) with n = 1000
Describe the effect on the confidence interval estimate of increasing the sample size.
The proportion of successes in a random sample of 400 was calculated as 50%. Estimate the population proportion with 95% confidence.
Repeat part (a) with p = 33%
Repeat part (a) with p = 10%
Discuss the effect on the width of the confidence interval estimate of reducing the sample proportion.
A statistics practitioner working for MLB wants to supply radio and television commentators with interesting statistics. He observed several hundred games and counted the number of times a runner on first base attempted to steal second base. He found there were 373 such events, of which 259 were successful. Estimate with 95% confidence the proportion of all attempted thefts of second base that are successful.
A dean of a business school wanted to know whether the graduates of her school used a statistical inference technique during their first year of employment after graduations. She…