Concept explainers
Recycling: Aluminum Cans One environmental group did a study of recycling habits in a California community. It found that 70% of the aluminum cans sold in the area were recycled.
(a) If 400 cans are sold today, what is the probability that 300 or more will be recycled?
(b) If the 400 cans sold, what is the probability that between 260 and 300 will be recycled?
(a)
To find:
The probabilitythat 300 or more cans will be recycled.
Answer to Problem 21CR
Solution:
The probability that 300 or morecans will be recycled is 0.0166
Explanation of Solution
Calculation:
We have random variable x having a normal distribution with mean
Now, the mean is
And standard deviation will be
Now, we calculate
By using formula for normal distribution:-
By using Table 3 from appendix:
The probability that 300 or more cans will be recycled is 0.0166.
(b)
To find:
The probability that between 260 and 300 canswill be recycled.
Answer to Problem 21CR
Solution:
The probabilitythat between 260 and 300cans will be recycled is 0.9750.
Explanation of Solution
Calculation:
We have random variable x having a normal distribution with mean
Now, we calculate
Now, mean and standard deviation are as
Further,
Thus, the desired probability is 0.9750.
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