Need help with Statisitcs.

Question

1. The weights of adult tuna are normally distributed with a mean of 90 lbs and an standard deviation of 20 lbs. If you catch an adult tuna, what is the probability that it weighs less than 70 lbs?
2. Test scores on a final exam are normally distributed with a mean of 70 and a standard deviation of 8. What percent of students scored between a 78 and an 86?
3. The lifespan of a shoes is normally distributed with a mean of 24 months and a standard deviation of 6 months. What is the probability that a new shoes would last between 18 and 30 months?

Answer 1

use the empirical rule: probability of being within 1, 2 or 3 standard deviations from the mean = 68-95-99.7 percent

68% are within 1 standard deviation from the mean of 90. 68% are between 70 and 110

half of 1-68 = 32/2 = 16% are less than 70. 16% chance the adult tuna weights less than 70 lbs.

if the test score mean is 70, the chance of a score being between 1 and 2 standard deviations from the mean = (95%-68%) = 27%/2 = 13.5% 13.5% chance the score is between 78 and 86

shoe will last within 1 standard deviation from the mean = 68%

mean = 24, standard deviation=6, 18 to 30 is the range of one standard deviation from the mean

24-6 = 18, 24+6= 30