Random variable X is drawn from a normal distribution with mean 13.59 and standard deviation 2.39.

1. Calculate the probability of X being less than 11.31.
2. What is the probability of X exceeding 12.52?
3. What is the probability of X lying between 13.75 and 15.09?
4. Verify your answers to parts 1 and 2 above using numerical sampling.
5. (Harder) verify your answers to part 3 above using numerical sampling.

A sociology class contains 10 Bernie fans and 8 Hilary fans. What is the probability of choosing 5 at random and having 2 Hilary fans?

B.How big of sample is need to estimate the mean time with a 95% confidence interval and a maximum error of 1? The time has a variance equal to 20.

C, The probability that a student likes statistics is .1. What is the probability that 5 or less students like stats in a class of 16?

Among all the car accidents last year, 492 deaths were reported in
the road of which 240 wore belts and 252 wore no belts. Of the 2334
people involved in serious accidents 1945 wore seat belts and the rest
no
to. Calculate the probability of dying by not wearing a belt

b. Calculate the probability of dying if you wear the belt

c. If a person dies in a car accident; What is the probability of
who will wear a seat belt?

Consider a binomial experiment with 20 trials and probability 0.35 of success on a single trial.

(a) Use the binomial distribution to find the probability of exactly 10 successes. (Round your answer to three decimal places.)

(b) Use the normal distribution to approximate the probability of exactly 10 successes. (Round your answer to three decimal places.)

(c) Compare the results of parts (a) and (b). These results are fairly different. These results are almost exactly the same.

Suppose that X is a Poisson random variable with λ=39.

Round your answers to 3 decimal places (e.g. 98.765).

(a) Compute the exact probability that X is less than 26.

(b) Use normal approximation to approximate the probability that X is less than 26.

Without continuity correction:

With continuity correction:

(c) Use normal approximation to approximate the probability that 52<X<78.

Without continuity correction:

With continuity correction:

The lengths of earthworms are normally distributed with a mean of 3.2 inches

and a standard deviation of 0.8 inches.

A. What is the probability that a sample of 40 worms has a mean length of at least 3 inches?

B. What is the probability that Freddy the earthworm is between 2.5 in and 4.0 in long?

C. If I dig up a random sample of 25 earthworms, what is the probability that the mean nl _______

length in the sample would be less than 3.5 inches?

Consider a binomial experiment with 15 trials and probability 0.55 of success on a single trial.

(a) Use the binomial distribution to find the probability of exactly 10 successes. (Round your answer to three decimal places.)


(b) Use the normal distribution to approximate the probability of exactly 10 successes. (Round your answer to three decimal places.)


(c) Compare the results of parts (a) and (b).

These results are fairly different.These results are almost exactly the same.  

An urn contains 10 red balls and 5 green balls. Balls are randomly selected, one at a time, with replacement, until a red one is obtained. What is the probability that exactly k draws are needed? What is the probability that at least k draws are needed? Define a random variable associated with this experiment. Determine its probability mass function and cumulative distribution function, sketch their graphs. Find the expectation, variance and standard deviation of X.