Question

Assume that X has a normal distribution, and find the indicated probability.

1. The mean is  = 85.0 and the standard deviation is s = 12.0.  Find the probability that X is greater than 101.8.
   1. 0.0808                          b.   0.9192                    c.   0.7881                     d.   0.2119
2. The mean is  = 42 and the standard deviation is s = 6.  Find the probability that X is less than 51.
   1. 0.0668                          b.   0.9901                    c.    0.9332                    d.   0.0099
3. The mean is  = 120 and the standard deviation is s = 13.2.  Find P(138  140).
   1. 0.8488                          b.   0.0226                    c.   0.1512                     d.   0.9774

Find the indicated Probability.

4. A bank’s loan office uses credit scores in their application process. The credit scores are normally distributed with a mean of 705 and a standard deviation of 55. If an applicant is randomly selected, find the probability of a rating that is between 760 and 820.

4. 1. 0.1404                          b.   0.6404                    c.   0.8596                                 d. 0.8413
5. A bank’s loan office uses credit scores in their application process. The credit scores are normally distributed with a mean of 705 and a standard deviation of 55. Applicants are offered loans if their credit scores are above 670. Find the probability that a randomly selected applicant will be offered a loan.

5. 1. 0.2611                          b.   0.3811                    c.   0.7389                     d.  0.0703
6. Scores on a test are normally distributed with a mean of 72.5 and a standard deviation of 9.1. Find , the test score which separates the bottom 80% from the top 20%. Round to the nearest tenth.

1. 51.3                             b.   64.9                         c.   80.1                        d. 93.7

7. In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 990 kWh and a standard deviation of 198 kWh. For a randomly selected home, find the probability that the September energy consumption level is between 1100 kWh and 1250 kWh.

1. 0.1926                          b.   0.3828                    c.   0.6178                     d. 0.8074

8. The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy lasts less than 270 days?

1. 0.4813                          b.   0.5517                    c.   0.50            d.  0.4483

Answer 1