Question

assume that admission to medical school is based only on a students mcat test score. the mcat test scores are normally distributed with a mean of 75 and a standard deviation of 6.5. if a student must be at the 95th percentile or higher, what is the lowest score a student can obtain and still be admitted to medical school?
a. 84.78
b. 86.62
c. 88.55
d. 85.66

Explanation:

Step1: Find z-score for 95th percentile

The z-score corresponding to the 95th percentile is $z = 1.645$ (standard normal distribution value).

Step2: Use z-score formula to find score

The z-score formula is $z = \frac{X - \mu}{\sigma}$, rearrange to solve for $X$: $X = \mu + z\sigma$
Substitute $\mu = 75$, $\sigma = 6.5$, $z=1.645$:
$X = 75 + (1.645)(6.5)$

Step3: Calculate the final score

$X = 75 + 10.6925 = 85.6925 \approx 85.66$

Answer:

d. 85.66