1.A distribution of values is normal with a mean of 60.1 and a standard deviation of 41.6. Find the probability that a randomly selected value is between -31.42 and 68.42. P(-31.42 < X < 68.42) =

2. Find a z-score for a data value of 19 if the mean of a set of data is 70 and the standard deviation is 16.5.

Round your answer to two decimal places.

3. What is the z-score of x=3x=3 if it is 2.62.6 standard deviations to the left of the mean? z=? What is the z-score of x=8x=8 if it is 2.72.7 standard deviations to the right of the mean? z=?

4. Suppose the random variable XX is normally distributed with mean 60 and standard deviation 5. Let ZZ be distributed according to the standard normal distribution. Then P(63.3

5.Suppose the random variable XX is normally distributed with mean 66 and standard deviation 9. Let ZZ be distributed acording to the standard normal distribution. Then P(X<62.58)P(X<62.58) is the same as P(Z<______<)). Round to two decimal places

6. Suppose the random variable XX is normally distributed with mean 70 and standard deviation 9. Let ZZ be distributed acording to the standard normal distribution. Then P(X>62.35)P(X>62.35) is the same as P(Z>_____). Round to two decimal places

7. In his MTH173 class, Professor Fibonacci found that the mean score of the first test was 67. Suppose that the scores are normally distributed with a standard deviation of 14 points. What is the probability that a randomly selected score is less than 46? P(x<46) = What is the probability that a randomly selected score is more than 57? P(x>57)) = what is the probability that a randomly selected score is between 46 and 57? P(46 =