Selecting Condiments A box of condiments has ten small packages, in which three are ketchup, three are mustard, and four are relish. A sample of three packages is randomly selected (without replacement) from the box.

1. Find the probability distribution for X, the number of mustard packages in the sample.

2. What are mean and variance of X?

Please explain steps

6)

One thousand people compete in an oyster-eating contest. Their scores (number of oysters eaten) are normally distributed with a mean of 51 and standard deviation of 11. What is the probability that a given individual will eat less than 29 or more than 72?

Select one:

( ) a. 98%

( ) b. 5%

( ) c. 13%

( ) d. 2%

( ) e. 47%

In a box of 5 balls, 2 are red and 3 are blue. Two balls are randomly selected (without replacement). Let X be the number of red balls in the two selected balls.

a. Find the probability distribution of X (i.e., list all possible values of X and their corresponding probabilities).

b. Find the expected value and the standard deviation of X.

An urn contains 6 white and 10 black balls. The figure gives by
the roll of a dice balance indicates the number of balls that will be drawn without delivery of the ballot box.
Let A be the event defined by:
A: all the balls drawn from the urn are white.
What is the probability that the dice has delivered a 3 knowing that A has realized (Use Bayes' Law)?

Suppose We put five different dice into a hat. The dice have the following number of side:4,6,8,12,20. When we choose a die from the hat, each of the five of the dice are equally likely to appear.

a) What is the probabilty that a “6” appears?

b) Now, suppose a “6” appears, what is the probability is was the 6-sided die that was chosen?

A tax auditor is selecting a sample of 5 tax returns for an audit. If 2 or more of these returns are​"improper," the entire population of 50 tax returns will be audited. Complete parts​ (a) through​ (e) below.

Q. What is the probability that the entire population will be audited if the true number of improper returns in the population is:

a) 15

b) 20

c) 5

d) 10

Soma recorded in the table the height of each player on the basketball team

Construct a normal probability distribution curve for this population! Indicate the number for the mean, 1SD, 2SD and 3SD (both sides of the mea) (1+ 6*0.5=4p)

The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 2643 miles, with a standard deviation of 368 miles. If he is correct, what is the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles? Round your answer to four decimal places.

Which element is proposed to have the highest third ionization energy.

Which age group reports the highest levels of stress?

Why?

Do you think this is true?