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Statistical Probability: Emergency Call Rates

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1. Let sample mean = 70 and the sample variance = 36 and assume the data is normally distributed. Use ths information to answer the following:

a. what is the median of this data set?
b. find an interval that would contain 68% of all data values from the sample.
c. find the x-value that corresponds to the 16th percentile
d. what is the z-score associated with x=80

2. In a certain city, the fire department typically responds to eight emergencies per month. Last month the department responded to two emergencies. Some of the employees at the fire station believe that because of last month's numbers, they are more likely to see above average emergency call rates this month. How would you respond to their position?

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Solution Summary

The emergency call rates for statistical probability is examined in the solution. The intervals and data values are determined.

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1. Let sample mean = 70 and the sample variance = 36 and assume the data is normally distributed. Use this information to answer the following:

A. What is the median of this data set?
Since the normal curve is symmetric with respect to its mean, the median will be equal to the mean mu=70.

B. Find an interval that would contain 68% of all data values from the sample.
Since the variance is 36, the standard deviation is sigma=root of 36=6. ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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