Question

the standard normal curve shown below models the population distribution of a random variable. What proportion of the values in the population dose not lie between the two z-scores indicated on the diagram?

Answer 1

Answer:

• 0.3175  or 31.75%

Explanation:

Please, find attached the diagram with the standard normal curve for this problem.

The two z-scores indiated are z = - 1.25 and z = 0.80

The proportion of the values in the population that does note lie between the two z-scores indicated on the diagram is equal to the the areas below the curve to the left of  z < -1.25 and to the right z > 0.80

The areas to the left or to the right of the z-scores are found in the tables of standard normal cummulative probabilities.

There are tables that show the cummulative probability to the left of the z-scores and tables that show the cummulative probability to the right of the z-scores.

Using a table for the cummulative probatility to the right of the z-score = 0.80 you find:

• P(Z > 0.80) = 0.2119

Using the symmetry property of the standard normal distribution, P(Z<-1.25) = P(Z>1.25).

Thus, using the same table: P(Z>1.25) = 0.1056

Hence, P(Z<-1.25) + P(Z>0.8) = 0.1056 + 0.2119 = 0.3175.

Therefore, 0.3175 or 31.75% of the values in the population does not lie between the two z-scores indicated on the diagram.