The average number of mosquitos in a stagnant pond is 80 per square meter with astandard deviation of 12. If 36 square meters are chosen at random for a mosquitocount, find the probability that the average of those counts is more than 81.6 mosquitosper square meter. Assume that the variable is normally distributed.

A)0.3%B)21.2%C)78.8%D)28.8%

It has been reported that 48% of teenagers play video games on their phones. A random sample of 60 teenages is drawn. Find the probability that the proportion of teenagers in the sample who play videos games on their phone is less than 0.500 . Write only a number as your answer. Round to 4 decimal places (for example 0.3748). Do not write as a percentage.

At a certain university, 50% of all entering freshmen planned to major in a STEM (science, technology, engineering, mathematics) discipline. A sample of 36 freshmen is selected. What is the probability that the proportion of freshmen in the sample is between 0.499 and 0.580? Write only a number as your answer. Round to 4 decimal places (for example 0.3748). Do not write as a percentage.

(FIXED) .Three symmetrical and homogeneous dice are tossed simultaneously. Find the probability of event A: the total number of dots appears at 10, given event B is at least one dice has upper face 3 dots. (the result of lesson is p(A|B) = p(AB)/p(B) = (15/6^3)/(91/6^3))

In a certain population of mussels (Mytilus edulis), 80% of the individuals are infected with an intestinal parasite. A marine biologist plans to examine 100 randomly chosen mussels from the population.

1. Find the probability that 85% or more of the sampled mussels will be infected using normal approximation to binomial distribution.
2. What is the expected number of infected mussels in 50 randomly chosen mussels?

Exercise 4. (20pts) Chocolate Bar Calories The average number of calories in a 1.5-ounce chocolate bar is 225. Suppose that the distribution of calories is approximately normal with σ = 10 . Find the probability that a randomly selected chocolate bar will have. (4a) Between 200 and 220 calories. Draw picture (4b) Less than 200 calories

2. A basketball player hits 80% of her free-throws. If she gets four (4) attempts, with what probability will she:

a. hit exactly three free-throws;

b. three or more free-throws;

c. one or more free-throws?

d. What is the expected number of free-throws she will hit? (The mean).

A recent study shows that 18% of adults in the US do not use the Internet. Suppose that 12 adults are randomly selected in the US.

a)Construct the PMF of X, the number of adults who don't use internet in this group.

b)What is the expected value and standard deviation of X?

c)What is the probability that at least 1 of the adults uses the Internet?

In the United States, 7.8% of the population has diabetes. The CDC compiles data from an SRS of 1200 people.

a.What would be the mean number of people who have diabetes from such a sample? What would be the standard deviation?

b.Use the Normal approximation to estimate the probability that at least 115 people (out of the 1200) would have diabetes?

A call centre manager in an insurance company is interested in knowing the pattern of calls for cancellation. The number of cancellation calls an agent receives per hour follows a Poisson distribution with a mean of 1.2.

What is the probability that an agent receives more than two cancellation calls for the next three hours?

a)0.3 b)0.823 c)0.7 d)0.177