My mom didn't realize she had left the bathtub running with the plug in. she was in a panic to get my baby sister to the hospital. we didn't discover the overflow until we returned home a few hours later. the surplus water had filled the heating vents. they made gurgling sounds whenever the heat came on.

a.
dirty

b.
extra

c.
cold

d.
noisy

a) In order to be eligible for Mensa, a person must have an IQ score of at least 130.81.

b) 2900 people are elegible for Mensa.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

(a) What IQ score should one have in order to be eligible for Mensa?

Scores in at least the 98th percentile, so scores of at least X when Z has a pvalue of 0.98. So at least X when Z = 2.054.

In order to be eligible for Mensa, a person must have an IQ score of at least 130.81.

(b) In a typical region of 145,000 people, how many are eligible for Mensa

Only 2% are elegible. So

0.02*145000 = 2900

2900 people are elegible for Mensa.