Based on experience, the manager of a credit card company reports that three out of every ten credit card applications are disapproved. Use the normal approximation to determine the probability that at most 50 of 200 new credit applications will be rejected.
use normal dist with sigma = 1, mean = 0.3 area below 50/200 = 0.25,
http://davidmlane.com/hyperstat/z_table.html
I get 0.48
How??? Solution and explanation pleaseeeee
Hey, plug and chug. I already took the course. It is your turn to learn how.
To solve this problem using the normal approximation, we need to calculate the mean and standard deviation first.
The mean (μ) is calculated by multiplying the probability of disapproval (0.3) by the sample size (200):
μ = 0.3 * 200 = 60
The standard deviation (σ) is calculated using the formula for the square root of the product of the probability of success (0.7) and the probability of failure (0.3) divided by the sample size:
σ = sqrt(0.7 * 0.3 * 200) = sqrt(42)
Now, using the normal distribution, we can calculate the probability that at most 50 of the 200 credit applications will be rejected.
We need to use a continuity correction since we are dealing with a discrete situation (number of credit applications). So, we need to calculate the probability that the number of rejected applications is less than or equal to 50.
P(X ≤ 50) = P(X < 50.5)
Converting this to a standard normal distribution, we subtract the mean (60) from the value we want to calculate the probability for (50.5), and divide it by the standard deviation (sqrt(42)):
Z = (50.5 - 60) / sqrt(42)
Using a standard normal table or calculator, we can find the probability associated with the Z-score.
Finally, we can determine the probability by finding the area to the left of the calculated Z-score.
P(X ≤ 50) = P(Z < calculated Z-score)