Question

Od. No matter how we change the standard deviation, if the mean stays 45 grams, the proportion of bags weighing less than 42 grams will not change. QUESTION 8 10 po Suppose scores on the mathematics section of the SAT follow a normal distribution with mean 540 and standard deviation 120. ACT math scores are normally distributed with a mean of 18 and a standard deviation of 8. What score on the ACT is equivalent to a score of 750 on the SAT? Give your answer as a whole number, e.g 13. Click Save and Submit to saue and submit. Click Save All Answers to save all answers Save All Answers MacBook Air 呂ロ F4 F5 F7 F8 F9 F10

Answer 1

Ans.

As given in the question that both Mathematics section of SAT and ACT math score follows a Normal distribution.

So, we need to find which ACT math score is equivalent to the SAT score. Using the information given in the question, we can find the ACT score which has the same Z-score for SAT.

Formula for Z-score:     $Z=\frac{x_{i}-\mu }{\sigma }=\frac{observation\:-true \:mean}{\sigma }$

For SAT:     $x_{i}=750,\:\:\mu =540,\:\:\sigma =120$

$Z=\frac{x_{i}-\mu }{\sigma }=\frac{750-540}{120}$

$Z=\frac{210}{120}$

$Z=1.75$

This is the Z-score for SAT for math score of 750, so now we have to find the observation for ACT math score for which Z-score is 1.75.

For ACT : $\mu =18,\:\:\sigma =8,\:\: z=1.75, \:\:x=?$

$Z=\frac{x_{i}-\mu }{\sigma }$

$1.75=\frac{x-18 }{8 }$

$1.75*8=x-18$

$\mathbf{x=32}$

So, the score of 32 in ACT is equivalent to the score of 750 in SAT.