Question

Suppose you are working with a data set that is normally distributed, with a mean of 150 and a standard deviation of 46. Determine the value of x from the following information. (Round your answers and z values to 2 decimal places.)

(a) 60% of the values are greater than x.

(b) x is less than 16% of the values.

(c) 25% of the values are less than x.

(d) x is greater than 65% of the values.

Answer 1

To determine the value of x in a data set that is normally distributed with a mean of 150 and a standard deviation of 46, we can use the z-score formula and the standard normal distribution table to find the corresponding values of x for different cumulative probabilities.

Step-by-step explanation:

To determine the value of x in a normal distribution with a mean of 150 and a standard deviation of 46, we can use the z-score formula and the standard normal distribution table.

(a) To find the value of x where 60% of the values are greater than x, we can find the z-score corresponding to a cumulative probability of 0.60 and use the formula z = (x - mean) / standard deviation to find x.

(b) To find the value of x where x is less than 16% of the values, we can find the z-score corresponding to a cumulative probability of 0.16 and use the formula z = (x - mean) / standard deviation to find x.

(c) To find the value of x where 25% of the values are less than x, we can find the z-score corresponding to a cumulative probability of 0.25 and use the formula z = (x - mean) / standard deviation to find x.

(d) To find the value of x where x is greater than 65% of the values, we can find the z-score corresponding to a cumulative probability of 0.65 and use the formula z = (x - mean) / standard deviation to find x.