91Ó°ÊÓ

For the standard normal distribution, find the area within \(1.5\) standard deviations of the mean-that is, the area between \(\mu-1.5 \sigma\) and \(\mu+1.5 \sigma\).

Find the area under the standard normal curve a. between \(z=0\) and \(z=1.95\) b. between \(z=0\) and \(z=-2.05\) c. between \(z=1.15\) and \(z=2.37\) d. from \(z=-1.53\) to \(z=-2.88\) e. from \(z=-1.67\) to \(z=2.24\)

Find the area under the standard normal curve a. to the right of \(z=1.36\) b. to the left of \(z=-1.97\) \(c .\) to the right of \(z=-2.05\) d. to the left of \(z=1.76\)

Determine the following probabilities for the standard normal distribution. a. \(P(-1.83 \leq z \leq 2.57)\) b. \(P(0 \leq z \leq 2.02)\) c. \(P(-1.99 \leq z \leq 0)\) d. \(P(z \geq 1.48)\)

Find the following probabilities for the standard normal distribution. a. \(P(z<-1.31)\) b. \(P(1.23 \leq z \leq 2.89)\) c. \(P(-2.24 \leq z \leq-1.19)\) d. \(P(z<2.02)\)

Find the following areas under a normal distribution curve with \(\mu=20\) and \(\sigma=4\). a. Area between \(x=20\) and \(x=27\) b. Area from \(x=23\) to \(x=26\) c. Area between \(x=9.5\) and \(x=17\)

Find the following areas under a normal distribution curve with \(\mu=12\) and \(\sigma=2\). a. Area between \(x=7.76\) and \(x=12\) b. Area between \(x=14.48\) and \(x=16.54\) c. Area from \(x=8.22\) to \(x=10.06\)

Let \(x\) denote the time taken to run a road race. Suppose \(x\) is approximately normally distributed with a mean of 190 minutes and a standard deviation of 21 minutes. If one runner is selected at random, what is the probability that this runner will complete this road race a. in less than 160 minutes? b. in 215 to 245 minutes?

A construction zone on a highway has a posted speed limit of 40 miles per hour. The speeds of vehicles passing through this construction zone are normally distributed with a mean of 46 miles per hour and a standard deviation of 4 miles per hour. Find the percentage of vehicles passing through this construction zone that are a. exceeding the posted speed limit b. traveling at speeds between 50 and 57 miles per hour

The Bank of Connecticut issues Visa and MasterCard credit cards. It is estimated that the balances on all Visa credit cards issued by the Bank of Connecticut have a mean of \(\$ 845\) and a standard deviation of \(\$ 270 .\) Assume that the balances on all these Visa cards follow a normal distribution. a. What is the probability that a randomly selected Visa card issued by this bank has a balance between \(\$ 1000\) and \(\$ 1440\) ? b. What percentage of the Visa cards issued by this bank have a balance of \(\$ 730\) or more?