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Marta_Voda [28]
3 years ago
13

The number of books borrowed from a library each week follows a normal distribution. When a sample is taken for several weeks, t

he mean is found to be 190 and the standard deviation is 30. There is a ___% chance that more than 250 books were borrowed in a week.
Mathematics
2 answers:
Marat540 [252]3 years ago
8 0
\mathbb P(X>250)=\mathbb P\left(\dfrac{X-190}{30}>\dfrac{250-190}{30}\right)=\mathbb P(Z>2)\approx0.0228

Or, if you're familiar with the empirical rule and the basic properties of the normal distribution, you can use the fact that approximately 95/% of the distribution lies within two standard deviations of the mean, or

\mathbb P(|Z|

which means about 5\% of the distribution lies outside this interval, or

\mathbb P((-22))\approx0.05

Because the distribution is symmetric, you have

\mathbb P(-22)
\implies \mathbb P((-22))=\mathbb P(-22)=2\mathbb P(Z>2)\approx0.05
\implies \mathbb P(Z>2)\approx 0.025
Mrac [35]3 years ago
5 0

Answer:

There is a 2.28% chance that more than 250 books were borrowed in a week.

Step-by-step explanation:

Given : The number of books borrowed from a library each week follows a normal distribution. When a sample is taken for several weeks, the mean is found to be 190 and the standard deviation is 30.

To find : There is a ___% chance that more than 250 books were borrowed in a week ?

Solution :

Formula to find z-score is

z=\frac{x-\mu}{\sigma}

Where, \mu=190 is the mean

\sigma=30 is the standard deviation

x=250 is the value

Substitute the value in the formula,

z=\frac{250-190}{30}

z=\frac{60}{30}

z=2

According to the normal distribution table,  P(z<2) = 0.9772

Now, The probability that more than 250 books were borrowed in a week will be

P(x>250)=P(z>2)= 1-P(z

Therefore, There is a 2.28% chance that more than 250 books were borrowed in a week.

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For the median you would arrange all the numbers in order from least to greatest and cancel one from the left and one from the right each time. Since there is no middle number, the closest would be 50 and 60. Thus you you add 50+60 and get 110 and then divide by 2 giving you 55.

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