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Tresset [83]
3 years ago
6

Seven customers enter a clothing store and are observed to determine if they will make a purchase. The store owner states that t

here is a 75% chance of a customer making a purchase. The random variable x represents a customer making a purchase. Calculate the mean, variance and standard deviation for the number of customers that make a purchase.
Mathematics
1 answer:
blondinia [14]3 years ago
3 0

Answer: Mean = 5.25

Variance = 1.3125

Standard deviation = 1.456

Step-by-step explanation:

The mean and variance of a binomial distribution with parameters n (number of trials) and p ( the probability of getting success in each trial) is given by :-

\text{Mean}=np\\\\\text{Variance}=np(1-p)

Given : The total number of enter a clothing store : n=7

The probability of a customer making a purchase= 0.75

Now,

\text{Mean}=7(0.75)=5.25\\\\\text{Variance}=7(0.75)(0.25)=1.3125\\\\\Rightarrow\ \text{Standard deviation}=\sqrt{1.3125}=1.14564392374\approx1.1456

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Answer:

X \sim N(61,14)  

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Since the distribution for X is normal then the distribution for the sample mean  is also normal and given by:

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\mu_{\bar X} = 61

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So then is appropiate use the normal distribution to find the probabilities for \bar X

Step-by-step explanation:

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Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

X \sim N(61,14)  

Where \mu=61 and \sigma=14

Since the distribution for X is normal then the distribution for the sample mean \bar X is also normal and given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

\mu_{\bar X} = 61

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So then is appropiate use the normal distribution to find the probabilities for \bar X

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Gnesinka [82]

Answer:

Simplify

Q-[R+S]-T

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10m+5n-24

Step-by-step explanation:

We have the expressions:

Q=7m+3n\\R=11-2m\\S=n+5\\T=-m-3n+8

Now, we need simplify:

Q-[R+S]-T

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We need to remember the rule of signs:

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+/+=+

With this in mind we solve the parentheses:

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let's group common terms

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We must add and subtract common terms:

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The answer is:

10m+5n-24

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