According to a U.S. Census American Community Survey, 5.69% of workers in Portland, Oregon, commute to work on their bicycles. Find to 4 decimal places the probability that in a sample of 300 workers from Portland, Oregon, the number who commute to work on their bicycles is 20 to 25.

Suppose that your enemy has a set of 20 weighted coins that each has a probability of 0.6 of landing heads when flipped. Estimate the mean number of heads if the set was flipped over and over by simulating 250,000 flips of the set and computing the average. (In python)

The number of orders that come into a mail-order sales office each month is normally distributed with a population mean of 298 and a population standard deviation of 15.4. For a particular sample size, the probability is 0.2 that the sample mean exceeds 300. How big must the sample be?

The number of days (X) after mailout it takes a utility company to receive payment for a customer’s bill is a normal random variable with a mean of 31 days and a standard deviation of 6 days. There is a probability of 0.50 that a bill will be received later than days after mailout.

Let Z be a standard Normal random variable. Define Za2 to be the number y such that P( Z > y ) = a (this is the standard definition).

What is P( Z < Zo.2 )?

(i.e. what is the probability that a standard Normal variable takes a value below Zo.2 ?)

1. A large protein of 1205 amino acids was produced errors of average 8 mistakes/200 amino acids.

Calculate probability to produce protein with:

1. No mutation
2. Less than 2 mutations
3. Exactly 3 mutations

Give mathematical expression and the number used in these expressions.

1. From a group of 50 basketball players, 5 are to be selected as centers, 10 as forwards, and 10 as guards. In how many ways can this selection be made?

2. If three balanced diced are rolled, find the probability that at least two show the same number.

A drawer contains six bags numbered 1-6, respectively i contains i blue balls and 6 green balls. You roll a fair die and then pick a ball out of a bag with the number shown on the die. What is the probability the ball is blue?

Suppose the local Best Buy store averages 301 customers every day entering the facility with a standard deviation of 80 customers. A random sample of 50 business days was selected. What is the probability that the average number of customers in the sample is between 290 and 310?

A is called a palindrome if it reads the same from left and right. For instance, 13631 is a palindrome, while 435734 is not. A 6-digit number n is randomly chosen. Find the probability of the event that

(a) n is a palindrome.

(b) n is odd and a palindrome.

(c) n is even and a palindrome.