Question

Given a normal distribution with A MEAN of 50 and standard deviation of 4, what is the probability that:

a. X > 45?

b. X < 43?

c. Six percent of the values are less than what X value?

d. Between what two X values (symmetrically distributed around the mean) are sixty-five percent of the values?

Answer 1

Solution:

We are given:

a. X > 45?

Answer: Using the z-score formula, we have:

Using the standard normal table, we have:

b. X < 43?

Answer: Using the z-score formula, we have:

Using the standard normal table, we have:

c. Six percent of the values are less than what X value?

Answer: We have to first find the z-value corresponding to area = 0.06. Using the standard normal table, we have:

Now using the z-score formula, we have:

d. Between what two X values (symmetrically distributed around the mean) are sixty-five percent of the values?

Answer: We have to first find z-score corresponding to area 0.35/2=0.175. Using the standard normal table, we have:

Now using the z-score formula, we have:

Next, we have to find the z-score corresponding to area 0.65 + 0.175 = 0.825. Using the standard normal table, we have:

Now using the z-score formula, we have:

Therefore, between 46.2616 and 53.7384 are sixty-five percent of the values.