91Ó°ÊÓ

The national average SAT score (for Verbal and Math) is 1028 . If we assume a normal distribution with \(\sigma=92,\) what is the 90th percentile score? What is the probability that a randomly selected score exceeds \(1200 ?\)

When is the normal distribution not a good approximation for the binomial distribution?

The average number of calories in a 1.5 -ounce chocolate bar is \(225 .\) Suppose that the distribution of calories is approximately normal with \(\sigma=10 .\) Find the probability that a randomly selected chocolate bar will have a. Between 200 and 220 calories b. Less than 200 calories

About what percentage of the area under the normal distribution curve falls within 1 standard deviation above and below the mean? 2 standard deviations? 3 standard deviations?

What does the central limit theorem say about the shape of the distribution of sample means?

Use the normal approximation to the binomial to find the probabilities for the specific value(s) of X. a. n = 30, p = 0.5, X = 18 b. n = 50, p = 0.8, X = 44 c. n = 100, p = 0.1, X = 12

Use the normal approximation to find the probabilities for the specific value(s) of X. a. \(n=10, p=0.5, X \geq 7\) b. \(n=20, p=0.7, X \leq 12\) c. \(n=50, p=0.6, X \leq 40\)

What are two other names for a normal distribution?

The average monthly mortgage payment including principal and interest is \(\$ 982\) in the United States. If the standard deviation is approximately \(\$ 180\) and the mortgage payments are approximately normally distributed, find the probability that a randomly selected monthly payment is a. More than \(\$ 1000\) b. More than \(\$ 1475\) c. Between \(\$ 800\) and \(\$ 1150\)

The average lifetime of smoke detectors that a company manufactures is 5 years, or 60 months, and the standard deviation is 8 months. Find the probability that a random sample of 30 smoke detectors will have a mean lifetime between 58 and 63 months.