Question

Adjusting the probability statement P(35.5 ≤ x ≤ 39.5) to the standard normal variable resulted in P(1.59 ≤ z ≤ 2.74). Recall that the normal probability table gives area under the curve to the left of a given z value. Use the table to find P(1.59 ≤ z ≤ 2.74), the probability that between 36 and 39 questions are answered correctly, rounding the result to four decimal places. P(1.59 ≤ z ≤ 2.74) = P(z ≤ 2.74) − P(z ≤ 1.59)

Answer 1

0.0529

Explanation:

Use the table to find P(1.59 ≤ z ≤ 2.74)

The z values of 1.59 and 2.74 are gotten from the formula,

z = (x - mean)/ standard deviation.

The probabilities that we are looking for are that of between 36 and 39.

Looking at the table, we look at each value if z separately.

The first one is

P(z = 1.59). Go to the normal distribution table,

We read up a value of 0.94408 by looking at the z column on the left for 1.5 and tracing it to where it coincides with z value of 0.09 at the top

P(z= 2.74) = 0.99693 by looking at the z column on the left for 2.7 and tracing it to where it coincides with z value of 0.04 at the top.

P(1.59 ≤ z ≤ 2.74) = P(z ≤ 2.74) − P(z ≤ 1.59) = 0.99693 - 0.94408

= 0.05285

= 0.0529 to 4 decimal places.