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Blizzard [7]
4 years ago
13

A survey found that the American family generates an average of 17.2 pounds of glass garbage trash each year. Assume the standar

d deviation of the ditribution is 2.5 pounds. Find the probability that the mean of a sample of 47 families will be between 16.6 and 17.6 pounds.
Mathematics
1 answer:
SIZIF [17.4K]4 years ago
6 0

Answer: 0.8137

Step-by-step explanation:

As per given , we have

\mu= 17.2\ ,\ \sigma=2.5

Sample size : n= 47

Let \overline{X} be the sample mean o.

Then, the probability that the mean of a sample of 47 families will be between 16.6 and 17.6 pounds will be :

P(16.6

=P(-1.645

[∵ z= \dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]

=P(z

=0.8636793-(1- 0.9500151)  [By using p-value calculator]

=0.8636793-0.0499849=0.8136944\approx0.8137

Hence, the probability that the mean of a sample of 47 families will be between 16.6 and 17.6 pounds= 0.8137

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4. A solution of 60% fertilizer is to be mixed with a solution of 21% fertilizer to form 234 liters of a 43% solution. How many
solniwko [45]

Given:

A solution of 60% fertilizer is to be mixed with a solution of 21% fertilizer to form 234 liters of a 43% solution.

To find:

The quantity of the 60% solution in the mixture.

Solution:

Let x be the quantity of the 60% solution and y be the quantity of the 21% solution.

Quantity of mixture is 234. So,

x+y=234

x=234-y                  ...(i)

The mixture has 43% fertilizer. So,

\dfrac{60}{100}x+\dfrac{21}{100}y=\dfrac{43}{100}\times 234

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