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
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
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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