Question

Math

Posted 3 months ago

```
In one online store, $12 \%$ of the orders are placed by new customers. Let $N$ 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 $N$.
Round your answers to one decimal place.
Mean: $\square$ orders
Standard deviation: $\square$ orders
```

Sign in to unlock the answer

Answer from Sia

Posted 3 months ago

Solution by Steps

step 1

To find the mean of the geometric distribution with probability $p = 0.12$, we use the formula $\mu = \frac{1}{p}$

step 2

Substituting $p = 0.12$ into the formula gives us $\mu = \frac{1}{0.12}$

step 3

Calculating the mean, we get $\mu = \frac{1}{0.12} = 8.33333$

step 4

To find the standard deviation of the geometric distribution, we use the formula $\sigma = \frac{\sqrt{1-p}}{p}$

step 5

Substituting $p = 0.12$ into the formula gives us $\sigma = \frac{\sqrt{1-0.12}}{0.12}$

step 6

Calculating the standard deviation, we get $\sigma = \frac{\sqrt{0.88}}{0.12} = 7.81736$

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 $p$ is given by $\frac{1}{p}$, and the standard deviation is given by $\frac{\sqrt{1-p}}{p}$. These formulas are used to calculate the expected number of trials until the first success and the variability of this number, respectively.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages

Strong algorithms that better know you

Early access to new release features

Study Other Question