To find the probability of a randomly selected adult female's pulse rate being less than 79 beats per minute, we calculate the Z-score using the provided mean and standard deviation, and then refer to a standard normal distribution table to find the corresponding probability.
The subject of this question falls under the category of Mathematics, more specifically, it relates to statistics and the concept of the normal distribution.
Given that adult female pulse rates are normally distributed with a mean of 76.0 beats per minute and a standard deviation of 12.5 beats per minute, we need to find the probability that a randomly selected adult female's pulse rate is less than 79 beats per minute.
To calculate this probability, we use the Z-score formula, which is Z = (X - μ) / σ, where X is the value we are interested in (79 beats per minute), μ is the mean (76.0 beats per minute), and σ is the standard deviation (12.5 beats per minute).
Step 1: Calculate the Z-score for 79 beats per minute.
Z = (79 - 76) / 12.5 = 0.24
Step 2: Use the standard normal distribution table, or a calculator with a normal distribution function, to find the probability that corresponds to a Z-score of 0.24.
Step 3: The probability of a pulse rate being less than 79 beats per minute is approximately 0.5948 (rounded to four decimal places).
The complete question is here:
Assume that females have pulse rates that are normally distributed with a mean of 76.0 beats per minute and a standard deviation of a 12.5 beat per minute Complete parts (a) through (c) below
a. if 1 adult female is randomly selected to the probability that her pulse rate is less than 79 beats per minute
The probability is
(Round to four decimal places as needed)