156k views
1 vote
The mean of a certain set of measurements is 27 with a standard deviation of 14. The distribution of the

data from which the sample was drawn is mound-shaped. The proportion of measurements that is less

than 13 is


Less than at least 3

4

.
Exactly 16%.

At least 16%.

At most 16%.

User Sir Ksilem
by
8.4k points

1 Answer

1 vote

Answer:

Exactly 16%.

Explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
\mu and standard deviation
\sigma, the z-score of a measure X is given by:


Z = (X - \mu)/(\sigma)

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 p-value, we get the probability that the value of the measure is greater than X.

The mean of a certain set of measurements is 27 with a standard deviation of 14.

This means that
\mu = 27, \sigma = 14

The proportion of measurements that is less than 13 is

This is the p-value of Z when X = 13, so:


Z = (X - \mu)/(\sigma)


Z = (13 - 27)/(14)


Z = -1


Z = -1 has a p-value of 0.16, and thus, the probability is: Exactly 16%.

User Shawn Patrick Rice
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories