3) Assume the random variable x is normally distributed with mean=84 and standard deviation=5. Find the indicated probability.

P(68

4) In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The responses were normally distributed, with a mean of 5.9 and a standard deviation of 2.5. Answer parts (a)-(c) below.

(a) Find the probability that a randomly selected study participant's response was less than 4.

The probability that a randomly selected study participant's response was less than 4 is ___. (Round to four decimal places as needed.)

(b) Find the probability that a randomly selected study participant's response was between 4 and 6.

The probability that a randomly selected study participant's response was between 4 and 6 is___. (Round to four decimal places as needed.)

(c) Find the probability that a randomly selected study participant's response was more than 8.

The probability that a randomly selected study participant's response was more than 8 is___. (Round to four decimal places as needed.)

5) In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 68.8 inches and a standard deviation of 3. inches. A study participant is randomly selected. Complete parts (a) through (c) below.

(a) Find the probability that a study participant has a height that is less than 67 inches.

The probability that the study participant selected at random is less than 67 inches tall is___. (Round to four decimal places as needed.)

(b) Find the probability that a study participant has a height that is between 67 and 71 inches.

The probability that the study participant selected at random is between 67 and 71 inches tall is___. (Round to four decimal places as needed.)

(c) Find the probability that a study participant has a height that is more than 71 inches.

The probability that the study participant selected at random is more than 71 inches tall is___. (Round to four decimal places as needed.)