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Question
Math
Posted 3 months ago

In one online store, 12%12 \% of the orders are placed by new customers. Let NN be the number of orders placed in a day to reach the store's first new customer. Assume each order's customer status is independent.

Find the mean and standard deviation of NN.
Round your answers to one decimal place.
Mean: \square orders

Standard deviation: \square orders
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Answer from Sia
Posted 3 months ago
Solution by Steps
step 1
To find the mean of the geometric distribution with probability p=0.12p = 0.12, we use the formula μ=1p\mu = \frac{1}{p}
step 2
Substituting p=0.12p = 0.12 into the formula gives us μ=10.12\mu = \frac{1}{0.12}
step 3
Calculating the mean, we get μ=10.12=8.33333\mu = \frac{1}{0.12} = 8.33333
step 4
To find the standard deviation of the geometric distribution, we use the formula σ=1pp\sigma = \frac{\sqrt{1-p}}{p}
step 5
Substituting p=0.12p = 0.12 into the formula gives us σ=10.120.12\sigma = \frac{\sqrt{1-0.12}}{0.12}
step 6
Calculating the standard deviation, we get σ=0.880.12=7.81736\sigma = \frac{\sqrt{0.88}}{0.12} = 7.81736
step 7
Round the mean and standard deviation to one decimal place: Mean = 8.3 orders, Standard deviation = 7.8 orders
1 Answer
Mean: 8.3 orders
Standard deviation: 7.8 orders
Key Concept
Geometric Distribution
Explanation
The mean of a geometric distribution with probability pp is given by 1p\frac{1}{p}, and the standard deviation is given by 1pp\frac{\sqrt{1-p}}{p}. These formulas are used to calculate the expected number of trials until the first success and the variability of this number, respectively.

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