All probabilty problems and corresponding chapters.

In a recent​ survey, it was found that the median income of families in country A was ​$57,900. What is the probability that a randomly selected family has an income greater than ​$57,900​?

5.1 .5, because it said median

Bob is asked to construct a probability model for rolling a pair of fair dice. He lists the outcomes as​ 2, 3,​ 4, 5,​ 6, 7,​ 8, 9,​ 10, 11, 12. Because there are 11​ outcomes, he​ reasoned, the probability of rolling a twelve must be 111. What is wrong with​ Bob's reasoning?

5.1 The experiment does not have equally likely outcomes.

In a certain card​ game, the probability that a player is dealt a particular hand is 0.4. Explain what this probability means. If you play this card game 100​ times, will you be dealt this hand exactly 40 times? Why or why​ not?

5.1 The probability 0.4 means that approximately 40 out of every 100 dealt hands will be that particular hand.​ No, you will not be dealt this hand exactly 40 times since the probability refers to what is expected in the​ long-term, not​ short-term.

Suppose you toss a coin 100 times and get 60 heads and 40 tails. Based on these​ results, what is the probability that the next flip results in a head​?

5.1 The probability that the next flip results in a head is approximately . 6.6.

You suspect a​ 6-sided die to be loaded and conduct a probability experiment by rolling the die 400 times. The outcome of the experiment is listed in the following table. Do you think the die is​ loaded? Why? (two number in the distribution are way above the others.)

5.1 Yes, bc two of the values have a higher prob of occurring than expected under the assumption of equally likely outcomes

What is the probability of an event that is​ impossible? Suppose that a probability is approximated to be zero based on empirical results. Does this mean that the event is​ impossible?

5.1, probability is 0, No

Is the following a probability​ model? What do we call the outcome ​"blue​"?

5.1, ​ .Impossible event if it is zero

A golf ball is selected at random from a golf bag. If the golf bag contains 3 green ​balls, 8 orange ​balls, and 9 yellow ​balls, find the probability of the following event. The golf ball is green or orange.

5.2

A probability experiment is conducted in which the sample space of the experiment is S={7,8,9,10,11,12,13,14,15,16,17,18}. Let event E={8,9,10,11,12,13} and event F={12,13,14,15}. List the outcomes in E and F. Are E and F mutually​ exclusive?

5.2

If events E and F are disjoint and the events F and G are​ disjoint, must the events E and G necessarily be​ disjoint? Give an example to illustrate your opinion.

5.2 No, events E and G are not necessarily disjoint. For​ example, E=​{0,1,2}, F=​{3,4,5}, and G=​{2,6,7} show that E and F are disjoint​ events, F and G are disjoint​ events, and E and G are events that are not disjoint.

According to a center for disease​ control, the probability that a randomly selected person has hearing problems is 0.148. The probability that a randomly selected person has vision problems is 0.084. Can we compute the probability of randomly selecting a person who has hearing problems or vision problems by adding these​ probabilities? Why or why​ not?

5.2 ​No, because hearing and vision problems are not mutually exclusive.​ So, some people have both hearing and vision problems. These people would be included twice in the probability.

According to a center for disease​ control, the probability that a randomly selected person has hearing problems is 0.145. The probability that a randomly selected person has vision problems is 0.097. Can we compute the probability of randomly selecting a person who has hearing problems or vision problems by adding these​ probabilities? Why or why​ not?

No, because hearing and vision problems are not mutually exclusive.​ So, some people have both hearing and vision problems. These people would be included twice in the probability.

The accompanying frequency polygon represents the number of a​ country's residents below 100 years of age. Complete parts​ (a) through​ (f) below. LOADING... Click the icon to view the frequency polygon. Its the one with -5, 5, 15, 25, etc.

(a) What is the class​ width? How many classes are represented in the​ graph? The class width is 1010. ​(Type a whole​ number.) There are 1010 classes represented in the graph. ​(Type a whole​ number.) ​(b) What is the midpoint of the first ​class? What are the lower and upper limits of the first ​class? Assume the lower and upper class limits are whole numbers. The midpoint of the first class is 55. ​(Type a whole​ number.) The lower limit of the first class is 00. The upper limit of the first class is 99. ​(Type whole​ numbers.) ​(c) What is the midpoint of the next to last ​class? What are the lower and upper limits of the next to last ​class? Assume the lower and upper class limits are whole numbers. The midpoint of the next to last class is 85. ​(Type a whole​ number.) The lower limit of the next to last class is 80. The upper limit of the next to last class is 89. ​(Type whole​ numbers.) ​(d) Which age group has the highest​ population? 30-39 ​(e) Which age group has the lowest​ population? 90-99 ​(f) Which age group has 47 ​million? 30-39

The most famous geyser in the​ world, Old Faithful in Yellowstone National​ Park, has a mean time between eruptions of 85 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 21.25 ​minutes, complete parts​ (a) through​ (f). What might you conclude if a random sample of 17time intervals between eruptions has a mean longer than 97 minutes? Select all that apply.

(a) What is the probability that a randomly selected time interval between eruptions is longer than 97 ​minutes? The probability that a randomly selected time interval is longer than 97 minutes is approximately . 2861. ​(Round to four decimal places as​ needed.) ​(b) What is the probability that a random sample of 6 time intervals between eruptions has a mean longer than 97 ​minutes? The probability that the mean of a random sample of 6 time intervals is more than 97 minutes is approximately 0.08330. ​(Round to four decimal places as​ needed.) ​(c) What is the probability that a random sample of 17 time intervals between eruptions has a mean longer than 97 ​minutes? The probability that the mean of a random sample of 17 time intervals is more than 97 minutes is approximately 0.00990. ​(Round to four decimal places as​ needed.) ​(d) What effect does increasing the sample size have on the​ probability? Provide an explanation for this result. The probability decreases decreases because the variability in the sample mean decreases decreases as the sample size increases. ​(e) What might you conclude if a random sample of 17 time intervals between eruptions has a mean longer than 97 ​minutes? Select all that apply. F. The population mean is 85 ​minutes, and this is just a rare sampling. This is the correct answer. G. The population mean is probably greater than 85 minutes. This is the correct answer. ​(f) On a certain​ day, suppose there are 22 time intervals for Old Faithful. Treating these 22 eruptions as a random​ sample, there is a 0.20 likelihood that the mean length of time between eruptions will exceed what​ value? The likelihood the mean length of time between eruptions exceeds 88.888.8 minutes is 0.20. ​(Round to one decimal place as​ needed.)

According to a study done by Nick Wilson of Otago University​ Wellington, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe​ people's habits as they sneeze. Complete parts​ (a) through​ (c).

6.2 (a) What is the probability that among 18 randomly observed​ individuals, exactly 5 do not cover their mouth when​ sneezing? Using the binomial​ distribution, the probability is . 2050. ​(Round to four decimal places as​ needed.) ​(b) What is the probability that among 18 randomly observed​ individuals, fewer than 6 do not cover their mouth when​ sneezing? Using the binomial​ distribution, the probability is 0.6571 ​(Round to four decimal places as​ needed.) ​(c) Would you be surprised​ if, after observing 18 ​individuals, fewer than half covered their mouth when​ sneezing? Why? Yes, it would be​ surprising, because using the binomial​ distribution, the probability is 0.0089​, which is less than 0.05. ​(Round to four decimal places as​ needed.)

Determine if the following probability experiment represents a binomial experiment. If​ not, explain why. If the probability experiment is a binomial​ experiment, state the number of​ trials, n. An experimental drug is administered to 110 randomly selected​ individuals, with the number of individuals responding favorably recorded.

6.2 Yes, because the experiment satisfies all the criteria for a binomial​ experiment, n=110.

Describe how the value of n affects the shape of the binomial probability histogram.

As increase, becomes more belled shaped

What effect does increasing the sample size have on the​ probability? Provide an explanation for this result.

The probability decreases because the variability in the sample mean decreases as the sample size increases.