On average, Nancy has noticed that 27 trucks pass by her apartment daily ( 24 hours). In order to find the probability that more than 1 truck will pass her apartment in a 2 -hour time period using the Poisson distribution, find the average number of trucks per 2 hours. Round your answer to three decimal places, if necessary.

The number of cars arriving at a servi-car or bank service window between 3:00 p.m. and 6:00 p.m. on Friday, a Poisson process follows at a rate of 0.25 cars per minute. Calculates the probability that fewer than 4 cars arrive at the bank between 4:00 p.m. and 4:10 p.m. (result at four decimal places)

A certain brand of toothpaste, Colcrest, is advertised as being preferred by 7 out of 10 dentists. Assume that this is true. A simple random sample of 6 dentists is taken.

a. Calculate the probability that 4 or fewer of the 6 dentists prefer Colcrest.

b. What is the average (or mean) number of dentists for this sample of size 6 who prefer Colcrest? What is the standard deviation?

A lottery is conducted in which 7 winning numbers are randomly selected from a total of 62 numbers (1-62). In addition, the Powerball, a single winning number, is selected from an independent pool of 26 numbers (1-26). You select 7 numbers from the pool of 62 numbers.

What is the probability that you will select at least one of the winning numbers?

Two candidates are running for​ president: John Democrat and Joe Republican. A recent survey concluded that John Democrat had a probability of 0.44 to win the election.Two hundred people are interviewed at random about whom they would vote for. A random variable X is defined as the number of people who said they would vote for John Democrat. Find the expected value of the random variable

2 peas are generated from parents having the green/yellow pair of genes, so there isa 0.75 probability that an individual pea will have a green pod. Find the probabilitythat the number of peas that has a green pod is

(a) at most 8

(b) fewer than 10

(c) more than half of the 12 peas

(d) between 7 to 10 (inclusive)

7. Suppose P(Z > z) = 0.9656. What is the value of z? Round your answer to 2 decimal places.

8. Let X be the number of shoppers in a supermarket line in an hour. Assume each person is independent. What type of probability distribution does X follow?

Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy adults, x is approximately normally distributed with mean of 38 and standard deviation of 12 . What is the probability that

a) x is less than 60?

b) x is between 16 and 60?

8. The mean number of fatal accidents between Mile markers 0 and 40 is 5 per year.

What is the probability there are a) exactly 3 fatalities b) less than 5 fatalities, c) 4 or less fatalities d) greater than 4 fatalities, greater e) Between 1 and 4 fatalities (10 points)

43​% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cashews are their favorite nut is​ (a) exactly​ three, (b) at least​ four, and​ (c) at most two. If​ convenient, use technology to find the probabilities.

P(3)=