Respuesta :
The mean and standard deviation will be 4 quotes and 3.46 quotes respectively
Mean and Standard Deviation
- A mean is the simple mathematical average of a set of two or more numbers
- The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance
What are steps to solve this problem?
The steps are given below:
- Sine we have a fixed number of successes and count the number of trials needed to obtain that first success, we have a geometric distribution.
- The mean and standard deviation of a geometric distribution can be calculated by using the formulae :
Mean = [tex]\frac{1}{p}[/tex]
Standard deviation = [tex]\frac{\sqrt{1-p}}{p}[/tex]
- Where p is the probability of success which is [tex]\frac{1}{4}[/tex] = 0.25 quotes
- So mean is [tex]\frac{1}{0.25}[/tex]= 4 quotes
- Standard deviation is [tex]\frac{\sqrt{1-\ 0.25}}{0.25}\ \approx\ \frac{0.866}{0.25}\ \approx3.464[/tex]
So the mean is 4 quotes and standard deviation will be 3.46 quotes
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