Question

A standardized mathematics test given to 14,000 students had the scores normally distributed. The mean was 850 and the standard deviation was 75. A student scoring below 775 points was deficient in mathematics. About how many students were rated deficient?

Answer 1

To find out how many students were rated deficient, we calculate the z-score corresponding to a score of 775 and find the proportion of the population that falls below that z-score.

Step-by-step explanation:

To find out how many students were rated deficient, we need to calculate the number of students who scored below 775 points. This can be done by finding the z-score corresponding to a score of 775 using the formula: z = (x - mean) / standard deviation. Plugging in the values, we get: z = (775 - 850) / 75 = -1.

Next, we can use a z-table or a calculator to find the proportion of the population that falls below a z-score of -1. The area to the left of -1 on the standard normal distribution table is approximately 0.1587.

Finally, to find the number of students rated deficient, we multiply the proportion by the total number of students: 0.1587 x 14,000 ≈ 2,220.5.