Among 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware, which is software programmed into the device (based on data from "Pacemaker and ICD Generator Malfunctions," by Maisel et al. , Journal of the American Medical Association, Vol. 295 , No. 16). If the firmware is tested in three different pacemakers randomly selected from this batch of 8834 and th e enti re batch is accepted if there are no fa ilures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?

Find the probabilities and indicate when the "5% guideline for cumbersome calculations" is used. In the same stud y cited in the preceding exercise, among the 47,637 patients transported by helicopter, 188 of them left the treatment center against medical advice, and the other 47,449 did not leave against medical advice. If 40 of the subjects transported by heli copter are randomly selected without replacement, what is the probability that none of them left the treatment center against medical advice?

Assuming boys and girls are equally​ likely, find the probability of a couple having a baby boy when their fifth child is​ born, given that the first four children were all boys

Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains (data from a QSR Drive-Thru Study). Assume that orders are randomly selected from those included in the table.

$$\begin{matrix} \text{ } & \text{McDonald's} & \text{Burger King} & \text{Wendy's} & \text{Taco Bell}\\ \text{Order Accurate} & \text{329} & \text{264} & \text{249} & \text{145}\\ \text{Order Not Accurate} & \text{33} & \text{54} & \text{31} & \text{13}\\ \end{matrix}$$

				 If two orders are selected, find the probability that they

are both fro m Taco Bell. Assume that the selections are made without replacement. Are the events independent?

If 25 people are randomly selected, find the probability that no 2 of them have the same birthday. Ignore leap years.

Subjects for the next presidential election poll are contacted using telephone numbers in which the last four digits are randomly selected (with replacement). Find the probability that for one such phone number, the last four digits include at least one 0.

It is generally recognized that it is wise to back up computer data. Assume that there is a 3% rate of disk drive failure in a year (based on data from various sources, including lifehacker.com). If all of your computer data are stored on a hard disk drive with a copy stored on a second hard disk dr ive, what is the probability that both drives will fail during a year?

Assume that different groups of couples use the XS ORT method of gender selection and each couple gives birth to one baby. The XSORT method is designed to increase the likelihood that a baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 36 couples. Find the mean and standard deviation for the numbers of girls in groups of 36 births.

Solve each equation.

$$7 a - 4 + 2 a = 3 a - 2$$

Most people can roll their tongues, but many can't. The ability to roll the tongue is genetically determined. Suppose we are interested in determining what proportion of students can roll their tongues. We test a simple random sample of 400 students and find that 317 can roll their tongues. The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to (a) 0.0008. (b) 0.02. (c) 0.03. (d) 0.04. (e) 0.05.

Shoppers in a large shopping mall are categorized as male or female, over 30 or 30 and under, and cash or credit card shoppers. In how many ways can the shoppers be categorized?

Find the $z_{\text {calc }}$ test statistic for each hypothesis test.

$$\bar{x}=8330, \mu_0=8,344, \sigma=48, n=36$$

Find

$$a. \ ( f \circ g ) ( x ) \ b. \ ( g \circ f ) ( x ) \ c. \ ( f \circ g ) ( 2 )$$

$$f ( x ) = 2 x - 3 , g ( x ) = \frac { x + 3 } { 2 }$$

What are the common pacemaker malfunctions?