Solutions only no work needs to be shown for the 4 questions.

1.Find the area under the standard normal curve betweenz=-1.67 and z=2.44 .

Round your answer to four decimal places.

A=

2.Obtain the area under the standard normal curve to the right of z=1.45 .

Round your answer to four decimal places.

A=

3.Find the z value for x=42 for a normal distribution with =30 and =5 .

Enter the exact answer.

z=

4.Compute probabilities.

Recall the following definitions from section 6.4 of the text.

The area under the normal curve from x = a to x = b with given mean and standard deviation is the probability that x assumes a value between x = a and x = b. If we are using Table IV in Appendix C, we need to standardize the random variable x using the formula z = (x )/, before using the table.

Alternatively, you may use a graphing calculator to obtain more accurate calculations without standardizing the random variable x.

For example, using a TI83 plus we calculate the area under the normal curve from x = a to x = b by using the

normalcdf(a,b,,)

where is the mean and is the standard deviation of the normal distribution. We use 1E99 for and 1E99 for , if needed.

Let x be a continuous random variable that is normally distributed with a mean of 23 and a standard deviation of 6 .

Round your answers to two decimal places.

(a) Standardize the variable value x = 27.0 .

z=

Standardize the variable value x = 53.0 .

z=