Find the area under the standard normal distribution:
1. between z =0 and z =0.56 answer = 0.2123
2. between z =0 and z = -2.07 answer = 0.4808
3.to the right of z =0.23 answer = 0.4090
4.to the right of z = -0.18 answer = 0.5714
5.between z = 0.79 and z = 1.28 answer = 0.1145
6. between z = -1.03 and z = 2.47 answer =0.8417
Applications of The Normal Curve
1. Suppose that the height of college women have a normal
distribution with mean mu = 65 inches and standard deviation sigma = 2.7 inches. What is
the probability that a randomly selected college woman is 62 inches or shorter?
Answer = .1335
2.From the previous problem, find the probably that a college woman selected
at random has a height greater than 68 inches. answer = .1335
3.If test scores on a statistic exam are normal with mean = 100 and standard
deviation sigma = 15, find the percent of scores that fall below 112. answer =
78.81%
4.The American Automobile Association reports that the average time it takes to respond to an emergency call is 25 minutes. Assume the variable is approximately normally distributed and the standard deviation is 4.5 minutes. If 80 calls are randomly selected, approximately how many will be responded to in less that 15 minutes? answer = 1.048 or approximately one call will be responded to in under 15 minutes.
5. In order to qualify for a police academy, candidates must score in the top 10% on a general abilities test. The test has a mean of 200 and a standard deviation of 20. Find the lowest possible score to qualify. Assume the test scores are normally distributed. answer = 226
Applications of The Central Limit Theorem2.The average number of pounds of meat a person consumes in a year is 218.4 pounds. Assume that the standard deviation is 25 pounds and the distribution is approximately normal. Find the probability that a person selected at random consumes less that 224 pounds per year. answer = 0.5871
3. From the previous problem, if a sample of 40 individuals is selected, find the probability that the mean of the sample will be less than 224 pounds. answer = 0.9222
Confidence Interval Estimation2.A random sample of 48 days taken at a large hospital shows that an average of 38 patients were treated in the emergency room per day. The standard deviation of the population is 4. Find a 99% confidence interval of the mean number of ER patients treated each day at the hospital. answer = [36.512,39.487]
3. Ten randomly selected automobiles were stopped, and the tread depth of the right front tire was measured. The mean depth was 0.32 inches, and the standard deviation was 0.08 inches. (a) Find a 95% confidence interval of the mean depth. Assume that that the variable is approximately normally distributed. answer = [0.26,0.38] (b) must the "t" distribution be used in this problem?
Minimum Sample Size to Estimate Population Mean MU
1.You want to estimate the mean weight of squirrels in your area. How any squirrels must be included in your sample if you want to be 95% confident that the sample mean weight is within 1 ounces of the population mean? You know that the population standard deviation is 5 ounces.
Answer: the margin of error is one ounce, the critical z score is 1.96,
and sigma =5 ounces. Calculating N:
Thus at least 96 squirrels should be included in your sample.