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1. Diastolic pressure below 70 ●○○○○ 10 ptsDiastolic blood pressures for men aged 35 to 44 are normally distributed with mean 80 mm Hg and standard deviation 10 mm Hg. What is the probability that a randomly chosen man in this age group has a diastolic blood pressure less than 70 mm Hg? Round to two decimal places.
2. Outlier percentage in a normal distribution ●●○○○ 20 ptsIn a normal distribution, a value is an outlier if it lies more than $1.5$ interquartile ranges above the upper quartile or more than $1.5$ interquartile ranges below the lower quartile. Using $z=\pm 0.67$ for the quartiles, what percent of values are outliers under this definition? Give the percent rounded to two decimal places.
3. Percentage of pitch times in an interval ●●○○○ 20 ptsTommy Wait's times between pitches are normally distributed with a mean of 36 seconds and a standard deviation of 2.5 seconds. What percentage of his times between pitches are between 30 and 34 seconds? Give the answer as a percentage, rounded to two decimal places.
4. Mean, spread and 90th percentile of heights ●●○○○ 20 ptsFor women athletes at UCLA, heights are approximately normal. The 25th percentile height is $62.5$ inches and the 75th percentile height is $65.5$ inches. Using $z=\pm 0.67$ for these quartiles, find the mean $\mu$ and the standard deviation $\sigma$ of the heights. Then, using $z=1.28$ for the 90th percentile, find the 90th percentile height. Round $\sigma$ and the 90th percentile height to two decimal places.
5. Proportion exceeding a rounded threshold ●●●○○ 50 ptsThe tensile strength of a metal component is normally distributed with mean $10000$ kg/cm² and standard deviation $100$ kg/cm². Each measurement is recorded to the nearest $50$ kg/cm². A measurement counts as exceeding $10150$ when its recorded value is greater than $10150$. What proportion of the measurements exceed $10150$ kg/cm²? Round to four decimal places.
6. Martian species height difference probability ●●●○○ 50 ptsSpecies 1 heights are normally distributed with mean 32 and variance 60. Species 2 heights are normally distributed with mean 22 and variance 70. A sample of 10 members of Species 1 and a sample of 14 members of Species 2 are drawn independently. Find the probability that the sample mean of Species 1 exceeds the sample mean of Species 2 by 5 or more. Round to three decimal places.