Let x be a binomial random variable with n=100 and p=.2. Find approximations to these probabilities: a. P(x$\gt$22) b. P(x$\geq$22) c. P(20$\lt$x$\lt$25) d. P(x$\leq$25)

a. Put the equation in slope-intercept form by solving for y. b. Identify the slope and the y-intercept. c. Use the slope and y-intercept to graph the line. 3x+y=0

Find these probabilities associated with the standard normal random variable z: a. P(z$\gt$5) b. P(-3$\lt$z$\lt$3) c. P(z$\lt$2.81) d. P(z$\gt$2.81)

Draw 100 random samples from a binomial distribution with parameters n=50 and p=.4. Consider an approximation to this distribution by a normal distribution with mean =np=4 and variance =npq=2.4. Draw 100 random samples from the normal approximation. Plot the two frequency distributions on the same graph, and compare the results. Do you think the normal approximation is adequate here?

The random variable X has a binomial distribution with n = 10 and p = 0.01. Determine the following probabilities. a. P(X = 5) b. P(X ≤ 2) c. P(X ≥ 9) d. P(3 ≤ X < 5)

Suppose the numbers of a particular type of bacteria in samples of 1 milliliter (ml) of drinking water tend to be approximately normally distributed, with a mean of 85 and a standard deviation of 9. What is the probability that a given 1-ml sample will contain more than 100 bacteria?

Let x be a binomial random variable with n=100 and p=.2. a. Use Table 1 in Appendix I to calculate P(4$\leq$x$\leq$6). b. Find $\mu$ and $\sigma$ for the binomial probability distribution, and use the normal distribution to approximate the probability P(4$\leq$x$\leq$6). Note that this value is a good approximation to the exact value of P(4$\leq$x$\leq$6) even though np=5.

An article in American Demographics claims that more than twice as many shoppers are out shopping on the weekends that during the week. Not only that, such shoppers also spend more money on their purchases on Saturdays and Sundays! Suppose that the amount of money spent at shopping centers between 4 P.M. and 6 P.M. on Sundays has a normal distribution with mean $85 and with a standard deviation of$20. A shopper is randomly selected on a Sunday between 4 P.M. and 6 P.M. and asked about his spending patterns. a. What is the probability that he has spent more than $95 at the mall? b. What is the probability that he has spent between$95 and $115 at the mall? c. If two shoppers are randomly selected, what is the probability that both shoppers have spent more than$115 at the mall?

A normal random variable x has mean $\mu$=1.2 and standard deviation $\sigma$=.15. Find the probability associated with each of the following intervals. a. 1.00$\lt$x$\lt$1.10 b. x$\lt$1.38 c. 1.35$\lt$x$\lt$1.50

Let z denote a standard normal random variable.

a. Find P (–1.66 < z < –0.48).

b. Find z0 such that P (-z0 ≤ z ≤ z0) = 0.901.

c. Find z0 such that P (z ≤ z0) = 0.0375.

d. Find z0 such that P (-z0 ≤ z ≤ z0) = 0.7698.

Consider a binomial random variable x with n=25 and p=.6. a. Can the normal approximation be used to approximate probabilities in this case? Why or why not? b. What are the mean and standard deviation of x? c. Using the correction for continuity, approximate P(x$\gt$9).

Let X be a binomial random variable with p = 0.2 and n = 20. Use the binomial table in Appendix A to determine the following probabilities. a. P(X ≤ 3) b. P(X > 10) c. P(X = 6) d. P(6 ≤ X ≤ 11)

Let x be the number of successes observed in a sample of n=5 items selected from a population of $N=10$. Suppose that of the N=10 items, M=6 are considered "successes." Find the probability. The probability of observing no successes

Evaluate the following absolute value expressions. a. |-100|-98, b. 5|2-8|, c. |-13|+|0|, d. 14-|-10+3|