91影视

Toss $4$times Suppose you toss a fair coin $4$times. Let $X=$the number of heads you get.

(a) Find the probability distribution of$X$.

(b) Make a histogram of the probability distribution. Describe what you see.

(c) Find $P(X鈮�3)$ and interpret the result.

Knees Patients receiving artificial knees often experience pain after surgery. The pain is measured on a subjective scale with possible values of 1 (low) to 5 (high). Let X be the pain score for a randomly selected patient. The following table gives part of the probability distribution for X.

(a) Find $P(X=5)$

(b) If two patients who received artificial knees are chosen at random, what鈥檚 the probability that both of them report pain scores of $1$or $2$? Show your work.

(c) Compute the mean and standard deviation of $X$. Show your work.

A test for extrasensory perception (ESP) involves asking a person to tell which of $5$shapes鈥攁 circle, star, triangle, diamond, or heart鈥攁ppears on a hidden computer screen. On each trial, the computer is equally likely to select any of the $5$shapes. Suppose researchers are testing a person who does not have ESP and so is just guessing on each trial. What is the probability that the person guesses the first $4$shapes incorrectly but gets the fifth correct?

a). $1/5$

b). ${\left(\frac{4}{5}\right)}^4$

c). ${\left(\frac{4}{5}\right)}^4\left(\frac{1}{5}\right)$

d). $\left(\frac{5}{1}\right){\left(\frac{4}{5}\right)}^4\left(\frac{1}{5}\right)$

e).$4/5$

Fire insurance Suppose a homeowner spends $\backslash (300$for a home insurance policy that will pay out $\backslash )200,000$if the home is destroyed by fire. Let $Y=$the profit made by the company on a single policy. From previous data, the probability that a home in this area will be destroyed by fire is $0.0002$.

(a) Make a table that shows the probability distribution of Y.

(b) Compute the expected value of Y. Explain what this result means for the insurance company

Using Benford's law According to Benford's law (Exercise $5$, page $353$), the probability that the first digit of the amount of a randomly chosen invoice is an $8$or a $9$is $0.097$. Suppose you examine randomly selected invoices from a vendor until you find one whose amount begins with an $8$or a $9$.

(a) How many invoices do you expect to examine until you get one that begins with an $8$or $9$? Justify your answer.

(b) In fact, you don't get an amount starting with an $8$or $9$until the ${40}^{th}$invoice. Do you suspect that the invoice amounts are not genuine? Compute an appropriate probability to support your answer.

In the previous exercise, the probability that at least $1$of Joe's $3$eggs contains salmonella is about

(a) $0.84$.

(b) $0.68$.

(c) $0.58$.

(d) $0.42$.

(e) $0.30$.

In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p?

(a)$n=10,p=0.5$

(b)$n=40,p=0.88$

(c)$n=100,p=0.2$

(d)$n=100,p=0.99$

(e)$n=1000,p=0.003$

To collect information such as passwords, online criminals use 鈥渟poofing鈥� to direct Internet users to fraudulent Web sites. In one study of Internet fraud, students were warned about spoofing and then asked to log in to their university account starting from the university鈥檚 home page. In some cases, the login link led to the genuine dialog box. In others, the box looked genuine but in fact was linked to a different site that recorded the ID and password the student entered. An alert student could detect the fraud by looking at the true Internet address displayed in the browser status bar below the window, but most just entered their ID and password. Is this study an experiment? Why? What are the explanatory and response variables?

As the dangers of smoking have become more widely known, clear class differences in smoking have emerged. British government statistics classify adult men by occupation as 鈥渕anagerial and professional鈥� ($43\%$of the population), 鈥渋ntermediate鈥� ($34\%$), or 鈥渞outine and manual鈥� ($23\%$). A survey finds that $20\%$of men in managerial and professional occupations smoke, $29\%$of the intermediate group smoke, and $38\%$in routine and manual occupations smoke.

(a) Use a tree diagram to find the percent of all adult British men who smoke.

(b) Find the percent of male smokers who have routine and manual occupations.

Spell-checking Refer to Exercise 3. Calculate the mean of the random variable X and interpret this result in context.