Question

the average early-bird special admission price for a movie is usd 5.81 with a standard deviation of usd 0.81. what is the probability that a randomly selected admission charge is less than usd 3.50?
which of the following statements holds true for this problem?
select the correct response:
the lower bound is located at the extreme right.
the mean of the distribution does not lie at $5.81.
the area that is of no interest to the reader is less than 0.5.
the value of the z score is negative.
the upper bound is located at the extreme right.
the area of interest is on the right side of the mean.
the value of the z score is positive.
my answer is not listed among the given choices.
the area of interest is greater than 0.5.

Explanation:

Step1: Recall z-score formula

$z = \frac{X - \mu}{\sigma}$

Step2: Plug in given values

$X=3.50$, $\mu=5.81$, $\sigma=0.81$
$z = \frac{3.50 - 5.81}{0.81} = \frac{-2.31}{0.81} \approx -2.85$

Step3: Evaluate the result

The z-score is negative, so this statement is true. Other options are false: the mean is $5.81$, the area of interest (left of $3.50$) is less than 0.5, and the z-score is not positive.

Answer:

The value of the z score is negative.