Need help with this one.
2 answers:
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Answer:
(a) The value of <em>x</em> is 5.
(b) The value of <em>y</em> is 15.
Step-by-step explanation:
Let the random variable <em>X</em> represent the number of electric toasters produced that require repairs within 1 year.
And the let the random variable <em>Y</em> represent the number of electric toasters produced that does not require repairs within 1 year.
The probability of the random variables are:
P (X) = 0.20
P (Y) = 1 - P (X) = 1 - 0.20 = 0.80
The event that a randomly selected electric toaster requires repair is independent of the other electric toasters.
A random sample of <em>n</em> = 20 toasters are selected.
The random variable <em>X</em> and <em>Y</em> thus, follows binomial distribution.
The probability mass function of <em>X</em> and <em>Y</em> are:
(a)
Compute the value of <em>x</em> such that P (X ≥ x) < 0.50:
Use the Binomial table for <em>n</em> = 20 and <em>p</em> = 0.20.
The least value of <em>x</em> that satisfies the inequality P (X ≥ x) < 0.50 is:
<em>x</em> - 1 = 4
<em>x</em> = 5
Thus, the value of <em>x</em> is 5.
(b)
Compute the value of <em>y</em> such that P (Y ≥ y) > 0.80:
Use the Binomial table for <em>n</em> = 20 and <em>p</em> = 0.20.
The least value of <em>y</em> that satisfies the inequality P (Y ≥ y) > 0.80 is:
20 <em>- y</em> = 5
<em>y</em> = 15
Thus, the value of <em>y</em> is 15.