A machine produces bolts which are 10% defective. Find the probability that in a sample of 400 bolts produced by this machine; (a) at most 30 bolts will be defective; (b) between 33 and 45 bolts are defective; (c) 55 or more bolts are defective.
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Prob. 33 to 45 of 400 defective, given 10% are defective
- Thread starter Godisgood
- Start date
Re: Probability
Here you are approximating binomial probability.
part c: at least 55
\(\displaystyle {\mu}= np=400(.1)=40\)
\(\displaystyle nq=n(1-p)=400(.9)=360\)
\(\displaystyle {\sigma}=\sqrt{npq}=\sqrt{400( .1) (.9)}=6\)
Using the continuity correction, you can rewrite the discrete probability \(\displaystyle P(x\geq 55)\)
as the continuous probability \(\displaystyle P(x\geq 54.5)\).
Draw the normal curve and label it with your data. \(\displaystyle {\mu}=40, \;\ {\sigma}=6\)
a shaded region to the right of 54.5. The z-score that corresponds to 54.5 is \(\displaystyle z=\frac{54.5-40}{6}\approx 2.41\overline{6}\)
So, the probability that at least 55 are defects is \(\displaystyle P(x\geq 54.5)=P(z\geq 2.416)=1-P(z\geq 2.416)=.00783\)
about a .78% probability of at least 55 being defective.
Now, you try the others. There is a nice spelled out example. Okey-doke?.
Here you are approximating binomial probability.
part c: at least 55
\(\displaystyle {\mu}= np=400(.1)=40\)
\(\displaystyle nq=n(1-p)=400(.9)=360\)
\(\displaystyle {\sigma}=\sqrt{npq}=\sqrt{400( .1) (.9)}=6\)
Using the continuity correction, you can rewrite the discrete probability \(\displaystyle P(x\geq 55)\)
as the continuous probability \(\displaystyle P(x\geq 54.5)\).
Draw the normal curve and label it with your data. \(\displaystyle {\mu}=40, \;\ {\sigma}=6\)
a shaded region to the right of 54.5. The z-score that corresponds to 54.5 is \(\displaystyle z=\frac{54.5-40}{6}\approx 2.41\overline{6}\)
So, the probability that at least 55 are defects is \(\displaystyle P(x\geq 54.5)=P(z\geq 2.416)=1-P(z\geq 2.416)=.00783\)
about a .78% probability of at least 55 being defective.
Now, you try the others. There is a nice spelled out example. Okey-doke?.
D
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Re: Probability
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Godisgood said:A machine produces bolts which are 10% defective. Find the probability that in a sample of 400 bolts produced by this machine; (a) at most 30 bolts will be defective; (b) between 33 and 45 bolts are defective; (c) 55 or more bolts are defective.
You have posted 5 problems - without showing a line of work.
Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.