Find the probability that:

Rolling a fair die 3 times, at least two dice are less than 4.

Previous answers have suggested 0.875 (189 feasible cases/ 216 total cases). However, from simple trial and error we can see that there are more than 27 cases where this answers fails. For example is the first dice gets a 4 and the 2nd dice gets 4,5,6 and the last dice gets any number, there is already 18 cases here that are not feasible.

Thank you.

63 % of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four.

(a) P(5)=____ (Round to three decimal places as needed.)

(b) P(x greater than or equals 6)=_____ (Round to three decimal places as needed.)

(c) P(x< 4)=___ (Round to three decimal places as needed.)

The number of students in the MPH program by county is given below. If a student is selected at random from this dataset, find the probability that:

MPH program (Show your work)

1. The student is from Escambia county
2. The student is from Santa Rosa county
3. The student is from either Escambia or Santa Rosa county
4. The student is not from Santa Rosa county

(Show your work)

1. Suppose that 24% of U.S. residents are fluent in a language other than English. Let X represent the number of people in a SRS of 12 U.S. residents who are fluent in another language.

1. (3 pts) What distribution will X have? (Give the name of this type of distribution.)

b. (4 pts) Find the mean and standard deviation of the distribution of X.

3. (6 pts) Calculate the probability that a random sample of 12 U.S. residents contains fewer than 3 who are fluent in a language other than English.

For each of the following statements, identify whether the statement is true or false, and explain why. Please limit each response to no more than 2 sentences.

a) The probability that a continuous random variable takes a specific value is 0.

b) Statistical inference is the process of drawing conclusions about unknown statistics by using known parameters.

c) The terms “histogram” and “bar graph” are synonyms.

d) If two events A and B are independent, then there is no overlap between the events on a Venn diagram.

e) The standard deviation of the number 10 is 1.

A Food Marketing Institute found that 34% of households spend more than $125 a week on groceries. Assume the population proportion is 0.34 and a simple random sample of 368 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.32?

Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.

Answer =  (Enter your answer as a number accurate to 4 decimal places.)

For each of the following statements, identify whether the statement is true or false, and explain why. Please limit each response to no more than 2 sentences.

1) The probability that a continuous random variable takes a specific value is 0.

2) Statistical inference is the process of drawing conclusions about unknown statistics by using known parameters.

3) The terms “histogram” and “bar graph” are synonyms.

4) If two events A and B are independent, then there is no overlap between the events on a Venn diagram.

5) The standard deviation of the number 10 is 1.

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 195.2-cm and a standard deviation of 0.8-cm. For shipment, 22 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is less than 195.1-cm.
P(M < 195.1-cm) =

Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.