You may need to use the appropriate appendix table or technology to answer this question. A binomial probability distribution has p = 0.20 and n = 100. (a) What are the mean and standard deviation?

)

What is the probability of exactly 24 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

(d)

What is the probability of 16 to 24 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

(e)

What is the probability of 15 or fewer successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

A game works as follows: the player rolls one dice once (let's call it ''n'') and then he rolls it second time (let's call this second roll "m'') and receives n^m points .

A)What is the probability that n = 1 knowing that the player has received more than 20 points.
b) What is the probability that m = 1 knowing that the player has received more than 20 points.
c) (What is the probability that the player receives more than 20 points?
d) Let X be the following random variable: X = n knowing that the player has received more than 20 points. Give the probability of X.

Health experts’ estimate for the sensitivity of coronavirus tests, as they are actually used, is 0.7. They also think the specificity is very high. Suppose specificity is 0.99 and that the health experts’ estimated sensitivity is correct (0.7).

a. In a population where 20% of the population is infected with the coronavirus, what is the probability that a person who tests positive actually is infected?

b. Continued. What is the probability that a person who tests negative actually is not infected?

c. If the prevalence of infection in the tested population is 0.8 (in other words, if 80% of people tested have the infection), what is the probability that a person who tests positive actually is infected?

d. Continued. What is the probability that a person who tests negative actually is not infected?

The mean time required to complete a certain type of construction project is 52 weeks with a standard deviation of 3 weeks. Answer questions 4–7 using the preceding information and modeling this situation as a normal distribution.

1. What is the probability of the completing the project in no more than 52 weeks?

1. 0.25
2. 0.50
3. 0.75
4. 0.05

2. What is the probability of the completing the project in more than 55 weeks?

1. 0.1587
2. 0.5091
3. 0.7511
4. 0.0546

3. What is the probability of completing the project between 56 weeks and 64 weeks?

1. 0.2587
2. 0.3334
3. 0.5876
4. 0.0911

4. What is the probability of completing the project within plus or minus one standard deviation of the mean?

1. 0.951
2. 0.852
3. 0.759
4. 0.683

The five most common words appearing in spam emails are shipping!, today!, here!, available, and fingertips!. Many spam filters separate spam from ham (email not considered to be spam) through application of Bayes' theorem. Suppose that for one email account, in every messages is spam and the proportions of spam messages that have the five most common words in spam email are given below.

shipping!        0.050      

today!             0.047

here!              0.034

Available       0.016

fingertips!      0.016

Also suppose that the proportions of ham messages that have these words are

Round your answers to three decimal places.

If a message includes the word shipping!, what is the probability the message is spam?

If a message includes the word shipping!, what is the probability the message is ham?

Should messages that include the word shipping! be flagged as spam?

b. If a message includes the word today!, what is the probability the message is spam?

If a message includes the word here!, what is the probability the message is spam?

Which of these two words is a stronger indicator that a message is spam?

Why?

Because the probability is

c. If a message includes the word available, what is the probability the message is spam?

If a message includes the word fingertips!, what is the probability the message is spam?

Which of these two words is a stronger indicator that a message is spam?

Why?

Because the probability is

d. What insights do the results of parts (b) and (c) yield about what enables a spam filter that uses Bayes' theorem to work effectively?

Explain.

It is easier to distinguish spam from ham when a word occurs in spam and less often in ham.

In a recent​ year, the total scores for a certain standardized test were normally​ distributed, with a mean of 500 and a standard deviation of 10.5. Answer parts ​(a)dash​(d) below. ​(a) Find the probability that a randomly selected medical student who took the test had a total score that was less than 489. The probability that a randomly selected medical student who took the test had a total score that was less than 489 is . 1474. ​(Round to four decimal places as​ needed.) ​(b) Find the probability that a randomly selected medical student who took the test had a total score that was between 498 and 511. The probability that a randomly selected medical student who took the test had a total score that was between 498 and 511 is . 3922. ​(Round to four decimal places as​ needed.) ​(c) Find the probability that a randomly selected medical student who took the test had a total score that was more than 523. The probability that a randomly selected medical student who took the test had a total score that was more than 523 is nothing. ​(Round to four decimal places as​ needed.) ​(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. A. The events in parts left parenthesis a right parenthesis and left parenthesis b right parenthesis are unusual because their probabilities are less than 0.05. B. The event in part left parenthesis a right parenthesis is unusual because its probability is less than 0.05. C. None of the events are unusual because all the probabilities are greater than 0.05. D. The event in part left parenthesis c right parenthesis is unusual because its probability is less than 0.05.  

Suppose a geyser has a mean time between eruptions of 74 minutes74 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 28 minutes28 minutes. What is the probability that a randomly selected time interval between eruptions is longer than 86 minutes? (b) What is the probability that a random sample of 15 time intervals between eruptions has a mean longer than 86 minutes? (c) What is the probability that a random sample of 32 time intervals between eruptions has a mean longer than 86 minutes? What effect does increasing the sample size have on the probability? Provide an explanation for this result. Fill in the blanks below. If the population mean is less than 8686 minutes, then the probability that the sample mean of the time between eruptions is greater than 8686 minutes ▼ decreases increases because the variability in the sample mean ▼ decreases increases as the sample size ▼ decreases. increases. (e) What might you conclude if a random sample of 32 time intervals between eruptions has a mean longer than 86 minutes? Select all that apply. A. The population mean is 74 , and this is just a rare sampling. B. The population mean must be more than 74 , since the probability is so low. C. The population mean may be less than 74. D. The population mean is 74 , and this is an example of a typical sampling result. E. The population mean may be greater than 74. F. The population mean cannot be 74 , since the probability is so low. G. The population mean must be less than 74, since the probability is so low.

The five most common words appearing in spam emails are shipping!, today!, here!, available, and fingertips!. Many spam filters separate spam from ham (email not considered to be spam) through application of Bayes' theorem. Suppose that for one email account, in every messages is spam and the proportions of spam messages that have the five most common words in spam email are given below.

shipping!        0.050      

today!             0.047

here!              0.034

Available       0.016

fingertips!      0.016

Also suppose that the proportions of ham messages that have these words are

Round your answers to three decimal places.

If a message includes the word shipping!, what is the probability the message is spam?

If a message includes the word shipping!, what is the probability the message is ham?

Should messages that include the word shipping! be flagged as spam?

b. If a message includes the word today!, what is the probability the message is spam?

If a message includes the word here!, what is the probability the message is spam?

Which of these two words is a stronger indicator that a message is spam?

Why?

Because the probability is

c. If a message includes the word available, what is the probability the message is spam?

If a message includes the word fingertips!, what is the probability the message is spam?

Which of these two words is a stronger indicator that a message is spam?

Why?

Because the probability is

d. What insights do the results of parts (b) and (c) yield about what enables a spam filter that uses Bayes' theorem to work effectively?

Explain.

It is easier to distinguish spam from ham when a word occurs in spam and less often in ham.