Question

The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability.The probability of no more than 35 defective CDs.The probability of no more than 35 defective CDs.

Answer 1

`P_B(X\leq35)=P_N(X<34.5)`

Explanation:

If we approximate the binomial distribution with a normal distribution, we have to apply a correction factor for the fact that we are now dealing with a continuous variable instead of a discrete one, as it was with the binomial distribution.

The probability of no more than 35 defective CDs: P(X<35)

In this case, as X=35 is not included in the interval, we start the interval from X=35-0.5=34.5.

`P_B(X\leq35)=P_N(X<34.5)`

being Pb the probability under the binomial distribution and Pn the probability under the normal distribution.

The area for the normal distribution is the one below X=34 (or P(X<34)).