Prob. 33 to 45 of 400 defective, given 10% are defective

[Godisgood]

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.

 

[galactus]

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?.

 

[Deleted member 4993]

Re: Probability

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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