Statistics and Probability Answers

What is the probability that sample mean is more than 12 million

If two dice are rolled one time, find the probability of getting these results.
a. A sum of 9
b. sum of 7 or 11
c. Doubles
d. A sum less than 9
e. A sum greater than or equal to 10

The lifetime of a certain type of automatic machine is normally distributed with mean and standard deviation equals to 3.1 and 1.1 years repspectivelly, use the standard normal table to find P left parenthesis x less than 3.3 right parenthesis

Assume that females have pulse rates are normally distributed with a mean of 76 bpm and a standard deviation of 12.5 bpm is 16 females randomly selected find the probability of pulse rates for the main less than 83 bpm

At a party, there are 100 cats. Each pair of cats flips a coin, and they shake paws if and only if the coin comes up heads. It is known that exactly 4900 pairs of cats shook paws. After the party, each cat is independently assigned a “happiness index” uniformly at random in the interval [0,1]. We say a cat is practical if it has a happiness index that is strictly greater than the index of every cat with which it shook paws. The expected value of the number of practical cats is m/n, where m and n are positive integers with gcd(m,n) = 1. Compute 100m+n.

Hong and Song each have a shuffled deck of eight cards, four red and four black. Every turn, each player places down the two topmost cards of their decks. A player can thus play one of three pairs: two black cards, two red cards, or one of each color. The probability that Hong and Song play exactly the same pairs as each other for all four turns is m/n, where m and n are positive integers with gcd(m,n) = 1.Compute 100m+n.

In a shipment of 20 computers, 2 are defective. Three computers are randomly selected and tested. What is the probability that all 2 are defective if the first one is not replaced after being tested?

which game would work with the Hypergeometric Distribution?

Let x, y, and z be nonnegative real numbers with x + y + z = 120. Compute the largest possible value of the median of the three numbers 2x + y, 2y + z, and 2z + x.

3) An airplane has 2 engines. P(malfunction) = .0004 for a single engine on a single flight and these malfunctions are independent. A flight will crash if both engines malfunction on that flight. The plane makes 3 roundtrips per day [which is 6 flights]. Find:
[hint: numbers like 4.95E-5 should be written as .0000495]

a) P(first engine use does not malfunction) =

b) P(first flight has no engine malfunctions) =

c) P(no engine malfunctions in first week) =

d) P(at least one engine malfunction in first year) =