To find the probability that a person scores higher than 72, we first need to convert the score of 72 to a z-score. The z-score is a measure of how many standard deviations an element is from the mean.

The formula to calculate the z-score is:

Z = (X - µ) / σ

Where:
X = raw score
µ = mean
σ = standard deviation

Given:
µ = 78
σ^2 = 36 (Therefore, σ = sqrt(36) = 6)
X = 72

Substituting these values into the formula, we get:

Z = (72 - 78) / 6 = -1

This means that a score of 72 is 1 standard deviation below the mean.

Next, we look up this z-score in the z-table, which gives the area to the left under the normal curve. The value for -1 is 0.1587. However, we want the probability that a person scores higher than 72, so we need to find the area to the right under the curve.

Since the total area under the curve is 1, the area to the right is:

1 - 0.1587 = 0.8413

So, the probability that a person taking the examination scores higher than 72 is 0.8413 or 84.13%.

Question

To find the probability that a person scores higher than 72, we first need to convert the score of 72 to a z-score. The z-score is a measure of how many standard deviations an element is from the mean.

The formula to calculate the z-score is:

Z = (X - µ) / σ

Where:
X = raw score
µ = mean
σ = standard deviation

Given:
µ = 78
σ^2 = 36 (Therefore, σ = sqrt(36) = 6)
X = 72

Substituting these values into the formula, we get:

Z = (72 - 78) / 6 = -1

This means that a score of 72 is 1 standard deviation below the mean.

Next, we look up this z-score in the z-table, which gives the area to the left under the normal curve. The value for -1 is 0.1587. However, we want the probability that a person scores higher than 72, so we need to find the area to the right under the curve.

Since the total area under the curve is 1, the area to the right is:

1 - 0.1587 = 0.8413

So, the probability that a person taking the examination scores higher than 72 is 0.8413 or 84.13%.

Knowee AI · Accepted Answer