Question

The scores on a test were normally distributed with a mean of 160 and a standard deviation of 9.44. A randomly selected student scored 176 on the test. What is the z-score that corresponds to the student's score of 176? Round to two decimal places.

Answer 1

To calculate the z-score for a test score of 176 with a mean of 160 and a standard deviation of 9.44, subtract the mean from the score (176 - 160 = 16) and then divide by the standard deviation (16 / 9.44 ≈ 1.6958), which results in a z-score of approximately 1.70 when rounded.

Step-by-step explanation:

The student has a question about how to calculate a z-score for a given score from a normal distribution. In this case, the z-score corresponding to a test score of 176 can be calculated using the formula z = (x - µ) / σ, where x is the score, µ is the mean of the distribution, and σ is the standard deviation. We are given that the mean (µ) is 160 and the standard deviation (σ) is 9.44.

To calculate the z-score for the student's score of 176:

• Subtract the mean from the score: 176 - 160 = 16.
• Divide the result by the standard deviation: 16 / 9.44 ≈ 1.6958.
• Round the result to two decimal places: z ≈ 1.70.

Therefore, the z-score that corresponds to the student's score of 176 is 1.70.