2) A happiness survey with normally distributed scores with mean 5.5 and standard deviation 2.3 was administered to IT workers in healthcare. a) Find the probability that a randomly selected participant’s response was greater than 5.



b) Find the probability that a randomly selected participant’s response was between 4.5 and 6.5.



c) Find the probability that the mean of a sample of 16 selected participant’s response was between 4.5 and 6.5.

2) A happiness survey with normally distributed scores with mean 5.5 and standard deviation 2.3 was administered to IT workers in healthcare. a) Find the probability that a randomly selected participant’s response was greater than 5.



b) Find the probability that a randomly selected participant’s response was between 4.5 and 6.5.



c) Find the probability that the mean of a sample of 16 selected participant’s response was between 4.5 and 6.5.

A newly developed test for coronavirus has sensitivity 0.90 and specificity 0.85. Sensitivity is the probability of a positive result given that a person has the virus, and specificity is the probability of a negative result given that a person has no virus. Suppose that 12% of the population has the coronavirus. If the test gives you a positive result, what is the probability that you actually have the virus? Show your work.

Suppose you have a three-sided die, the die is loaded
so that the probability of 1 or 2 coming out is the same and equal to
one
4 while the third side has a probability of 1
two
. If it is launched
twice the die is X the random variable that returns the sum of the
obtained results, write the table for the distribution function of
probability p for the random variable X.

Two six-sided dice are rolled. (Enter your probabilities as fractions.)

(a) What is the probability that the sum of the numbers is greater than eight? Correct: 5/18

(b) What is the probability that the sum of the numbers is greater than eight, given that the first die is a 4???

(c) What is the probability that the first die shows a 4, given that the sum of the numbers is greater than eight???

Determine the radius r of a sphere centered on the nucleus within which the probability of finding the electron for the ground state of hydrogen is 53 % .

Determine the radius r of a sphere centered on the nucleus within which the probability of finding the electron for the ground state of hydrogen is 95 % .

Determine the radius r of a sphere centered on the nucleus within which the probability of finding the electron for the ground state of hydrogen is 99 %.

The population mean and standard deviation are given below. Find the indicated probability and determine whether a sample mean in the given range below would be considered unusual. If convenient, use technology to find the probability. For a sample of n=3636, find the probability of a sample mean being less than 12, 752 or greater than 12,755 when μ =12,752 and σ =1.5

(1 point) A game of chance involves rolling an unevenly balanced 4-sided die. The probability that a roll comes up 1 is 0.13, the probability that a roll comes up 1 or 2 is 0.48, and the probability that a roll comes up 2 or 3 is 0.47 . If you win the amount that appears on the die, what is your expected winnings? (Note that the die has 4 sides.)

A biased coin has probability p = 3/7 of flipping heads. In a certain game, one flips this coin repeatedly until flipping a total of four heads.

(a) What is the probability a player finishes in no more than 10 flips?

(b) If five players independently play this game, what is the probability that exactly two of them finish in no more than ten flips?

Heights of fences are normally distributed with a mean of 52 inches and a standard deviation of 4 inches.

1. Find the probability that one randomly selected fence is under 54 inches.

2. Find the probability that two randomly selected fences are both under 54 inches.

3. Find the probability that the mean height of 4 randomly selected fences is under 54 inches.