# Standard Normal Distribution Assignment

1) Find the area of the indicated region under the standard normal curve.

2) Find the area under the standard normal curve to the left of z = 1.25. (click here for the diagram)

3) Use the standard normal distribution to find P (-2.25 < z < 0). 4) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individualʹs IQ score is found to be 90. Find the z-score corresponding to this value.

5) Find the z-scores for which 90% of the distributionʹs area lies between -z and z.

6) The distribution of room and board expenses per year at a four-year college is normally distributed with a mean of \$5850 and standard deviation of \$1125. Random samples of size 20 are drawn from this population and the mean of each sample is determined. Which of the following mean expenses would be considered unusual?

7) The amounts of time employees of a telecommunications company have worked for the distributed with a mean of 5.1 years and a standard deviation of 2.0 years. Random samples of size 18 are drawn from the population and the mean of each sample is determined. Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution.

8) A student answers all 48 questions on a multiple-choice test by guessing. Each question has four possible answers, only one of which is correct. Find the probability that the student gets exactly 15 correct answers. Use the normal distribution to approximate the binomial distribution.

9) If the probability of a newborn child being female is 0.5, find the probability that in 100 births, 55 or more will be female. Use the normal distribution to approximate the binomial distribution.

10) An airline reports that it has been experiencing a 15% rate of no-shows on advanced reservations. Among 150 advanced reservations, find the probability that there will be fewer than 20 no-shows.

11) A telemarketer found that there was a 1% chance of a sale from his phone solicitations. Find the probability of getting 5 or more sales for 1000 telephone calls.

12) Use a standard normal table to find the z-score that corresponds to the 30th percentile.