91Ó°ÊÓ

State the properties of the standard normal curve.

Explain why normal probability plots should be linear if the data are normally distributed.

Under what circumstances can the normal distribution be used to approximate binomial probabilities?

Find the indicated areas. For each problem, be sure to draw a standard normal curve and shade the area that is to be found. Determine the area under the standard normal curve that lies to the right of (a) \(Z=-3.01\) (b) \(Z=-1.59\) (c) \(Z=1.78\) (d) \(Z=3.11\)

Assume the random variable \(X\) is normally distributed with mean \(\mu=50\) and standard deviation \(\sigma=7 .\) Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded. $$P(40

Assume the random variable \(X\) is normally distributed with mean \(\mu=50\) and standard deviation \(\sigma=7 .\) Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded. $$P(55 \leq X \leq 70)$$

Find the indicated areas. For each problem, be sure to draw a standard normal curve and shade the area that is to be found. Determine the area under the standard normal curve that lies between (a) \(Z=-2.04\) and \(Z=2.04\) (b) \(Z=-0.55\) and \(Z=0\) (c) \(Z=-1.04\) and \(Z=2.76\)

Assume the random variable \(X\) is normally distributed with mean \(\mu=50\) and standard deviation \(\sigma=7 .\) Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded. $$P(40 \leq X \leq 49)$$

Find the indicated areas. For each problem, be sure to draw a standard normal curve and shade the area that is to be found. Determine the area under the standard normal curve (a) to the left of \(Z=-2\) or to the right of \(Z=2\) (b) to the left of \(Z=-1.56\) or to the right of \(Z=2.56\) (c) to the left of \(Z=-0.24\) or to the right of \(Z=1.20\)

Find the indicated areas. For each problem, be sure to draw a standard normal curve and shade the area that is to be found. Determine the area under the standard normal curve (a) to the left of \(Z=-2.94\) or to the right of \(Z=2.94\) (b) to the left of \(Z=-1.68\) or to the right of \(Z=3.05\) (c) to the left of \(Z=-0.88\) or to the right of \(Z=1.23\)