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Alisiya [41]
3 years ago
14

A Starbucks coffee shop serves an average of 3500 customers per day, with a standard deviation of 250. What is the probability t

hey will serve between 3300 and 4000 customers on any given day
Mathematics
2 answers:
hram777 [196]3 years ago
7 0

Answer:

Probability they will serve between 3300 and 4000 customers on any given day is 0.7654.

Step-by-step explanation:

We are given that a Starbucks coffee shop serves an average of 3500 customers per day, with a standard deviation of 250.

Assuming the data follows normal distribution.

<em>Firstly, Let X = No. of customers served by Starbucks coffee shop</em>

The z score probability distribution for is given by;

         Z = \frac{ X - \mu}{\sigma} ~ N(0,1)

where, \mu = population mean = 3500

            \sigma = standard deviation = 250

Probability that they will serve between 3300 and 4000 customers on any given day is given by = P(3300 < X < 4000) = P(X < 4000) - P(X \leq 3300)

          P(X < 4000) = P( \frac{ X - \mu}{\sigma} < \frac{4000-3500}{250} ) = P(Z < 2) = 0.97725

          P(X \leq 3300) = P( \frac{ X - \mu}{\sigma} \leq \frac{3300-3500}{250}) = P(Z \leq -0.8) = 1 - P(Z < 0.8)

                                                                 = 1 - 0.78814 = 0.21186

<em>Therefore, P(3300 < X < 4000) = 0.97725 - 0.21186 = 0.7654</em>

Hence, probability that they will serve between 3300 and 4000 customers on any given day is 0.7654.

castortr0y [4]3 years ago
6 0

Answer:

P(3300  

And we can find this probability with this difference:  

P(-0.8  

Step-by-step explanation:

Previous concepts  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem  

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

X \sim N(3500,250)  

Where \mu=3500 and \sigma=250  

We are interested on this probability  

P(3300  

And the best way to solve this problem is using the normal standard distribution and the z score given by:  

z=\frac{x-\mu}{\sigma}  

If we apply this formula to our probability we got this:  

P(3300  

And we can find this probability with this difference:  

P(-0.8  

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