Concept explainers
the mean and standard deviation of this distribution
Answer to Problem 62E
The required mean and standard deviation are 0.4348min and 1.1087min respectively.
Explanation of Solution
Given:
R less than one minute to brush the teeth 40% of the time
Spends more than two minutes brushing his teeth 2% of the time
Calculation:
It is given that the amount of time Ricardo spends brushing his teeth follows a
Ricardo spends less than one minute brushing his teeth about 40% of the time. He spends more than two minutes brushing his teeth 2% of the time.
That is, P (brushing teeth for less than one minute) = 0.40 and the z value corresponding to 0.40 probability from standard normal table is
Also, P (brushing teeth for more than two minutes) = 0.02. Then, brushing teeth for less than two minutes is 98% = 0.98. The z value corresponding to 0.98 probability from standard normal table is 2.054.
The following graph illustrates the given information to set up two equations in two unknowns.
Then, we can find the values of unknown mean and standard deviation using the following two equations as follows:
Multiplying both sides of the equations by and subtracting yields
or
Substituting this value back into equation (1), we obtain
or
Hence, the required mean and standard deviation are 0.4348min and 1.1087min respectively.
Conclusion:
Hence, the required mean and standard deviation are 0.4348min and 1.1087min respectively.
Chapter 2 Solutions
The Practice of Statistics for AP - 4th Edition
Additional Math Textbook Solutions
Essentials of Statistics, Books a la Carte Edition (5th Edition)
Introductory Statistics (10th Edition)
Statistical Reasoning for Everyday Life (5th Edition)
Elementary Statistics (13th Edition)
Basic Business Statistics, Student Value Edition (13th Edition)
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