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Safeway stocks national brands of coffee, as well as its own house brand. Consider a single randomly selected customer purchasing coffee and let "success" = the customer purchases a national brand. Assume p = 0.75, and that customers make coffee purchase decisions independently of one another. Also, assume that X = number among 20 randomly selected coffee purchasers who select a national brand, and that the random variable X follows the binomial distribution.
a. What is the probably that at most 15 customers choose a national brand?
b. What is the probability that exactly 15 customers choose a national brand?
c. What is the probability that at least 12 customers select a national brand?
d. Calculate the mean (i.e., the expected value) and the variance of the random variable X.
The world record time (in minutes) in the marathon is plotted versus the year in which the record was set for men and women separately. The plotting symbol o is used for men and x for women. The data include only records set between 1908 and 1988.
A random sample of 225 SAT scores has a mean of 1522. Assume that SAT scores have a population standard deviation of 300. construct a 95% confidence interval estimate of the mean SAT scores.
Suppose Napoleon were using Bayes' theorm to revise his information. To do so, he would have had to make some judgements about P(Prussian and English Join forces |Napoleon Wins) and P(Prussian and English Join forces |Napoleon loses).
Inventories represent a considerable investment for every organization; thus, it is important that they be managed well. Excess inventories can indicate poor financial and operational management.
There are 25 students in a probability class. Assume that there are 365 days in each year, and that the birthrate is constant throughout the year.
What is the probability that a cereal would either high calorie or high fiber? In other words, what is P(high calorie or high fiber)?
Here are fifty observations on the weight of tea bags. Calculate the Standard Deviation and Variance.
A radio station wants to know if residents in their area are in favor of a proposed tax increase. They invite listeners to call in to respond to the poll. 645 of the 800 who responded were against the tax.
What is an appropriate sample space for this experiment?
If the test contains 250 questions, what is the probability that Julie will score 75% or lower? (Use the normal approximation to the sampling distribution to solve this problem.)
Where should the warranty limits be set so that only 10% of the TVs need repairs at the manufacturer's expense?
The rate of defects among CD players of a certain brand is 1.1%. Use the Poisson approximation to the binomial distribution to find the probability that among 240 such CD players received by a store, there is at most one defective CD player.
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