Question

given a normal distribution with a mean of 50 and a standard deviation of 4. what is the probability that x > 43?
in the above problem, which of the following statements is true?
select the correct response:
the mean of the distribution lies on the 75th percentile.
my answer is not listed among the given choices.
the shaded region or area of interest occupies less than half of the area under the curve.
the mean of the distribution lies on the 25th percentile.
the shaded region or area of interest occupies more than half of the area under the curve.
the area of no interest to the problem solver is greater than 0.5.
the value of the mean is 4.
the computed z will lie on the right side of the mean.

Explanation:

Step1: Calculate z-score

$z = \frac{x - \mu}{\sigma} = \frac{48 - 50}{4} = -0.5$

Step2: Find $P(x>48)$

$P(x>48) = P(z>-0.5) = 1 - P(z<-0.5)$
From z-tables, $P(z<-0.5)=0.3085$, so $P(x>48)=1-0.3085=0.6915$

Step3: Evaluate statements

0.6915 > 0.5, so the area of interest is more than half the curve.

Answer:

The shaded region or area of interest occupies more than half of the area under the curve.