10. According to the article "Are Babies Normal?" by Traci Clemons and Marcello Pagano published in The American Statistician, Vol. 53, No. 4, pp. 298-302, the birth weights of babies are normally distributed with a mean of 3398 grams and a standard deviation of 575 grams.

1. What is the probability that a randomly selected baby weighs between 3100 grams and 3500 grams? Round your answer to 4 decimal places.
2. What is the probability that the average weight of 30 randomly selected babies is between 3100 grams and 3500 grams? Round your answer to 4 decimal places.
3. Why did the probability increase?

• The probability increased since the sample size increased and the sample means are more concentrated near the mean of 3398.
• The probability increased since the sample size increased and the distribution of sample means is more spread out.

8. The wingspans of adult herons are approximately normally distributed with a mean of 120 cm and a standard deviation of 11.2 cm.

1. Determine the proportion of herons that have wing spans less than 101 cm. Round your answer to 4 decimal places.
2. The largest 5 percent herons have wingspans of _____ cm or more. Round your answer to 1 decimal place.
3. The middle 75 percent of herons have wingspans between _____ and _____ cm. Round your answers to 1 decimal place. Put the smaller answer on the left and the larger answer on the right.
4. Determine the proportion of herons which have wingspans between 108 and 137 cm. Round your answer to 4 decimal places.
5. Determine the proportion of herons which have wingspans greater than 140 cm. Round your answer to 4 decimal places.
6. The smallest 15 percent of herons have wingspans of _____ cm or less. Round your answer to 1 decimal place

7. For a standard normal distribution, compute the following probabilities. Round answer to at least 4 decimal places. a) P(Z > -1.5) =

b) P(-2.2 < Z < -0.95) =

c) P(Z < 0.42) =

d) P(Z2.05) =