91Ó°ÊÓ

Calculate the area under the standard normal curve to the left of these values: a. \(z=1.6\) b. \(z=1.83\) c. \(z=.90\) d. \(z=4.18\)

Find the following probabilities for the standard normal random variable \(z\): a. \(P(-1.431.34)\) e. \(P(z<-4.32)\)

Find these probabilities for the standard normal random variable \(z\) : a. \(P(z<2.33)\) b. \(P(z<1.645)\) c. \(P(z>1.96)\) d. \(P(-2.58

Find the following percentiles for the standard normal random variable \(z\) : a. 90 th percentile b. 95 th percentile c. 98 th percentile d. 99 th percentile

A normal random variable \(x\) has mean \(\mu=10\) and standard deviation \(\sigma=2\). Find the probabilities of these \(x\) -values: a. \(x>13.5\) b. \(x<8.2\) c. \(9.4

A normal random variable \(x\) has mean \(\mu=1.20\) and standard deviation \(\sigma=.15 .\) Find the probabilities of these \(x\) -values: a. \(1.001.38\) c. \(1.35

The meat department at a local supermarket specifically prepares its " 1 -pound" packages of ground beef so that there will be a variety of weights, some slightly more and some slightly less than 1 pound. Suppose that the weights of these "1pound" packages are normally distributed with a mean of 1.00 pound and a standard deviation of .15 pound. a. What proportion of the packages will weigh more than 1 pound? b. What proportion of the packages will weigh between .95 and 1.05 pounds? c. What is the probability that a randomly selected package of ground beef will weigh less than .80 pound? d. Would it be unusual to find a package of ground beef that weighs 1.45 pounds? How would you explain such a large package?

Human heights are one of many biological random variables that can be modeled by the normal distribution. Assume the heights of men have a mean of 69 inches with a standard deviation of 3.5 inches. a. What proportion of all men will be taller than \(6^{\prime} 0^{\prime \prime}\) ? (HINT: Convert the measurements to inches.) b. What is the probability that a randomly selected man will be between \(5^{\prime} 8^{\prime \prime}\) and \(6^{\prime} 1^{\prime \prime}\) tall? c. President George \(\mathrm{W}\). Bush is \(5^{\prime} 11^{\prime \prime}\) tall. Is this an unusual height? d. Of the 42 presidents elected from 1789 through 2006,18 were \(6^{\prime} 0^{\prime \prime}\) or taller. \(^{1}\) Would you consider this to be unusual, given the proportion found in part a?

The diameters of Douglas firs grown at a Christmas tree farm are normally distributed with a mean of 4 inches and a standard devia- tion of 1.5 inches. a. What proportion of the trees will have diameters between 3 and 5 inches? b. What proportion of the trees will have diameters less than 3 inches? c. Your Christmas tree stand will expand to a diameter of 6 inches. What proportion of the trees will not fit in your Christmas tree stand?

Cerebral blood flow (CBF) in the brains of healthy people is normally distributed with a mean of 74 and a standard deviation of 16 a. What proportion of healthy people will have CBF readings between 60 and \(80 ?\) b. What proportion of healthy people will have CBF readings above \(100 ?\) c. If a person has a CBF reading below \(40,\) he is classified as at risk for a stroke. What proportion of healthy people will mistakenly be diagnosed as "at risk"?