Suppose the scores on an exam are normally distributed with a mean μ = 75 points, and standard deviation σ = 8 points.The instructor wanted to "pass" anyone who scored above 69. What proportion of exams will have passing scores? 0.1587 0.75 0.2266 0.7734 −0.75

To solve this problem, we need to use the concept of Z-scores in statistics. A Z-score measures how many standard deviations an element is from the mean.

Step 1: Calculate the Z-score for the score of 69. The formula for the Z-score is:

Z = (X - μ) / σ

where: X is the score, μ is the mean, and σ is the standard deviation.

Substituting the given values:

Z = (69 - 75) / 8 = -0.75

Step 2: Look up this Z-score in the Z-table to find the proportion of scores below 69. The value corresponding to -0.75 in the Z-table is 0.2266.

Step 3: Since we want the proportion of exams with passing scores (i.e., scores above 69), we subtract the proportion of scores below 69 from 1 (since the total probability is 1).

So, the proportion of exams with passing scores is 1 - 0.2266 = 0.7734.

Therefore, 0.7734 or 77.34% of exams will have passing scores.

To solve this problem, we need to convert the score of 69 to a z-score. The z-score is a measure of how many standard deviations an element is from the mean.

The formula for calculating the z-score is:

Z = (X - μ) / σ

where: X is the score, μ is the mean, and σ is the standard deviation.

Substituting the given values into the formula, we get:

Z = (69 - 75) / 8 = -0.75

Next, we need to find the proportion of exams that have a z-score greater than -0.75. We can do this by looking up -0.75 in the z-table, which gives us the proportion of exams that have a z-score less than -0.75.

The value for -0.75 in the z-table is 0.2266. However, this is the proportion of exams that scored below 69. To find the proportion of exams that scored above 69, we subtract this value from 1:

1 - 0.2266 = 0.7734

So, the proportion of exams that will have passing scores is 0.7734 or 77.34%.

To solve this problem, we need to use the concept of Z-scores in statistics. A Z-score measures how many standard deviations an element is from the mean.

Step 1: Identify the given values. The mean (μ) = 75 The standard deviation (σ) = 8 The score we are interested in (X) = 69

Step 2: Calculate the Z-score. The formula for calculating the Z-score is: Z = (X - μ) / σ Substituting the given values into the formula, we get: Z = (69 - 75) / 8 = -0.75

Step 3: Look up the Z-score in the Z-table. The Z-table gives us the proportion of data up to the given Z-score. For Z = -0.75, the proportion is approximately 0.2266. However, this gives us the proportion of exams that scored BELOW 69.

Step 4: Find the proportion of exams that scored ABOVE 69. Since the total proportion is 1, the proportion of exams that scored above 69 is: 1 - 0.2266 = 0.7734

So, the proportion of exams that will have passing scores is 0.7734.

To solve this problem, we need to use the concept of Z-scores in statistics. A Z-score measures how many standard deviations an element is from the mean.

Step 1: Identify the mean (μ), standard deviation (σ), and the score we are interested in (X), which in this case is 69.

Step 2: Calculate the Z-score using the formula Z = (X - μ) / σ.

Substituting the given values into the formula, we get Z = (69 - 75) / 8 = -0.75.

Step 3: Look up the Z-score in the Z-table to find the proportion of scores below the score of interest. The value corresponding to -0.75 in the Z-table is 0.2266.

However, since we are interested in the proportion of exams with passing scores (scores above 69), we need to subtract the value we found from 1 (since the total probability under the normal curve is 1).

So, 1 - 0.2266 = 0.7734.

Therefore, the proportion of exams that will have passing scores is 0.7734 or 77.34%.