Please use this as a reference when solving the problems below

In this lesson we will consider probabilities of randomly selected groups of data.

As a review and for reference, let's find the probability of one randomly selected person having and IQ of less than 90.

Step 1: Convert the 90 to a standard normal z.

z=x-/ x =90 =100 =15

z=90-100/15 = -10/15 -0.67

Step 2: Take the z of -0.67 to the table and find the probability of 0.2514.

Step 3: Since the table values are always from the left tail up, 0.2514 is the probability of less than 90.

Conclusion:

The probability that one randomly selected person has an IQ under 90 is 0.2514, 25%.

Now show your work:

1) IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Nine people are randomly selected. What is the probability that the average of their 9 IQ scores is less than 110?

2) Men's weights are normally distributed with a mean of 189lbs and a standard deviation of 39lbs. Four men are randomly selected. What is the probability that the average of their 4 weights is more than 195lbs?

3) Women's heights are normally distributed with a mean of 63.7 inches and a standard deviation of 2.6 inches. Seven women are randomly selected. What is the probability that the average of their 7 heights is more than 66 inches?

4) Women's weights are normally distributed with a mean of 171lbs and a standard deviation of 46lbs. If one woman is randomly selected, what is the probability that her weight is less than 150lbs?

5) Mensa International calls itself "the international high IQ society," and has more than 100,000 members. Membership requires an IQ score over 130.5. If one person is randomly selected, what is the probability that he/she is eligible for Mensa membership?