X:y=5:3 and x+y=56 work out the value of x-y
1 answer:
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Answer:
32 ft
Step-by-step explanation:
From the diagram, the side opposite the 60° angle is 28 feet.
We are looking for the approximate length of the cable.
The approximate length of the cable is the hypotenuse of the triangle shown.
Recall the sine ratio from SOH-CAH-TOA
Which means Sine of the angle is Opposite/Hypotenuse
Let the hypotenuse be h, then we have:
The length of the cable is approximately 32 feet
Answer:
The probability that at least 14 of the chips will be defective is 0.6664.
Step-by-step explanation:
The complete question is:
A manufacturing process produces semiconductor chips with a known failure rate of 5.4%. If a random sample of 300 chips is selected, approximate the probability that at least 14 will be defective. Use the normal approximation to the binomial with a correction for continuity .
Solution:
Let <em>X</em> = number of defective chips.
The probability that a chip is defective is, <em>p</em> = 0.054.
A random sample of <em>n</em> = 300 chips is selected.
A chip is defective or not is independent of the other chips.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 300 and <em>p</em> = 0.054.
But the sample selected is too large.
So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
- np ≥ 10
- n(1 - p) ≥ 10
Check the conditions as follows:
Thus, a Normal approximation to binomial can be applied.
So, .
Compute the probability that at least 14 of the 300 chips will be defective as follows:
Use continuity correction:
P (X ≥ 14) = P (X > 14 + 0.50)
= P (X > 14.50)
*Use a <em>z</em>-table for the probability.
Thus, the probability that at least 14 of the chips will be defective is 0.6664.
