What is the 10th percentile, n of group of people's pulse rates, where X = pulse rates of group of people, for which the mean is 73 and the standard deviation is 8? Assume a normal distribution. (Round your answer to the nearest whole number.)
n = .
To find the 10th percentile (n) of a group of people's pulse rates, we can use the standard normal distribution and the Z-score formula.
The Z-score formula is given by:
Z = (X - μ) / σ
where:
Z is the Z-score
X is the given pulse rate
μ is the mean pulse rate
σ is the standard deviation of the pulse rates
In this case, we are given that the mean (μ) is 73 and the standard deviation (σ) is 8.
To find the Z-score corresponding to the 10th percentile, we need to find the value of X that satisfies the equation:
Z = (X - μ) / σ = -1.28
We can rearrange the equation to solve for X:
X = Z * σ + μ
Substituting the values, we have:
X = -1.28 * 8 + 73
X = -10.24 + 73
X = 62.76
Since we are asked to round the answer to the nearest whole number, the 10th percentile (n) of the group of people's pulse rates is approximately 63.