1. A particular fruit's weight is normally distributed, with a mean of 497 grams and a standard deviation of 36 grams. If you pick one of these fruits at random, what is the probability that it will weigh between 479 grams and 543.8 grams. (Round your final answer to 3 places after the decimal point.)

2. A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 120 and a standard deviation of 8.2. Find the value of the score at the 45^th percentile (P₄₅).

Round your answer 2 places after the decimal point.

3. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 10.2 years, and standard deviation of 2.3 years. The 6.68% of items with the shortest lifespan will last less than how many years? (Round your final answer to 1 place after the decimal point.)

4. The amount of juice in bottles labeled as containing 28 ounces is normally distributed with a mean of 28.95 ounces and a standard deviation of 1.89 ounces. What proportion of bottles are filled with less than 28 ounces of juice?

Round your answer to 4 places after the decimal point.

5. The final exam in a certain course has scores that are normally distributed with a mean of 73.2 with a standard deviation of 8.2. If 39 students are randomly selected, find the probability that the mean of their final exam scores is less than 71.

Round your answer 4 places after the decimal point.

6. The weights of the fish in a certain lake are normally distributed with a mean of 19.8 pounds and a standard deviation of 5.6 pounds. If 5 fish are randomly selected, find the probability that the mean weight is between 15.1 and 23.1 pounds.

Round your answer 4 places after the decimal point.

7. Use the normal distribution to approximate the desired probability.

Find the probability that in 212 tosses of a single 19-sided die, we will get at least 8 threes.

Round your answer to 4 places after the decimal point.