Please note that the steps show rounded numbers, but that the final answers to the problems are calculated without rounding.
| Problem | Part | Solution |
|---|---|---|
| 1 | A | 0.19- Unusual (\(z= -2.088\)) |
| 1 | B | 0.225- Not Unusual (\(z = -1.059\)) |
| 1 | C | 0.325- Not Unusual (\(z = 1.882\)) |
| 1 | D | 0.335- Unusual (\(z = 2.176\)) |
| 2 | - | The probability that a randomly selected professional baseball player will have a batting average that is greater than 0.335 is 0.015. |
| 3 | - | The Normal Density curve is symmetric and has a bell shape. It is determined by its mean and standard deviation. |
| 4 | - | z: tells how many standard deviations away from the mean a certain observation lies. x: an observed data point. \(\mu\): mean of the population. \(\sigma\): standard deviation of the population. |
| 5 | - | For any bell-shaped distribution, 68% of the data will lie within 1 standard deviation of the mean, 95% of the data will lie within 2 standard deviations of the mean, and 99.7% of the data will lie within 3 standard deviations of the mean. This is called the 68-95-99.7% Rule for Bell-shaped Distributions. Needs to be at least three sentences. |
| 6 | A | \(\mu=150.8\) \(\sigma=8.8\) |
| 6 | B | \(P(X > 165) = P(z > 1.6136) = 0.0533\) |
| 6 | C | \(z = -1.2816\); this is Not Unusual. See question 1. |
| 6 | D | GRE score = 139.5, which rounds to 140. |
| 7 | A | \(\mu = 1800\) \(\sigma = 600\) |
| 7 | B | \(P(X > 2500) = P(z > 1.1667) = 0.1217\) |
| 7 | C | \(P(X < 2500) = P(z < 1.1667) = 0.8783\) This answer is easier to get by subtracting the answer to part (a) from 1. |
| 7 | D | \(P(X < 1500) = P(z < -0.5) = 0.3085\) |
| 7 | E | \(P( 1500 < X < 2500 ) = 0.5698\) |
| 7 | F | \(3^{rd}\) quartile of the speeds of hydrogen = 2204.4 \(\frac{m}{s}\) |
| 8 | A | Not normal |
| 8 | B | Not Normal |
| 8 | C | Normal |
| 8 | D | Normal |
| 8 | E | Not Normal |
| 8 | F | Normal |