The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 73 minutes and a standard deviation of 15 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible.
Find the Inter Quartile Range (IQR) for time spent at the hot springs.
Q1: minutes
Q3: minutes
IQR: minutes
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
Expert Solution
The variable X is the amount of time that person spent at Grover Hot Springs which follows normal distribution with mean 73 minutes and standard deviation 15 minutes.
The first quartile is,
The probability 0.25 would be converted to z score can be obtained using the excel formula “=NORM.S.INV(0.25)”. The z score value is –0.6745.
The required value is,
Comparing on both sides.
The first quartile is 62.8825 minutes.
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