Question

Note: All work must be shown, all answers simplified, in order to get credit.

1. Determine the area/probability under the normal distribution curve if:
a. ? = −2.04 1a. b. ? = 1.78 1b.

2. Determine the z-value associated with a probability of:
a. 0.9292 2a. b. 0.2327 2b.

3. Determine the z-values associated with the middle 72% of the 3. normal distribution.

      

4. Scores on a history test have an average of 80 with a standard deviation of 6. What is the probability that a student earned less than an 87 on the test? Answer in a sentence.

Answer 1

Dear student, we can solve one question at a time, please help to upload other questions separately. Here, I am still answering questions 1 and 2.

1.

a)

z = - 2.04

We need to check its corresponding value in the z-table.

Check for - 2 in the column and 0.04 in thee rows.

The value comes out to be 0.0207. This is the probability at the z-score of - 2.04.

b)

When z = 1.78

The value comes to be 0.9625.

2.

a)

We need to check this value in the z-table and get the z-score for this.

It comes out to be 1.47.

b)

It comes out to be -0.73.