find the normal approximation for the binomial probability that x=5,where n=12, and p=0.7compare probability to table b of normal distributions of table 2.
The only thing that i know so far is that p(x=5) is equivalent to 0.29. how would i complete this question? please clarify answer.
mary
We do not have access to "table b" or "table 2."
To find the normal approximation for the binomial probability with x = 5, n = 12, and p = 0.7, you first need to calculate the mean (μ) and the standard deviation (σ) of the binomial distribution.
The mean is given by μ = n * p, so in this case, μ = 12 * 0.7 = 8.4.
The standard deviation is calculated using the formula σ = sqrt(n * p * (1 - p)), where sqrt denotes the square root. Plugging in the values, σ = sqrt(12 * 0.7 * (1 - 0.7)) ≈ 1.337.
Once you have the mean and standard deviation, you can use the normal distribution to approximate the binomial probability.
First, standardize the binomial random variable x = 5 using the formula:
z = (x - μ) / σ
Plugging in the values from above, z = (5 - 8.4) / 1.337 ≈ -2.54.
Now, you need to compare this standardized value of z to the values in Table B of the normal distribution. This table provides the probabilities associated with different values of z.
Find the closest value of z in Table B and then look up the corresponding probability. Note that Table B usually provides probabilities for positive values of z, so you may need to locate the probability associated with the negative value (-2.54 in this case) and subtract it from 0.5 to get the correct probability.
After finding the probability from Table B, compare it to the binomial probability of 0.29. If they are close or equal, then the normal approximation is valid. Otherwise, the normal approximation may not be accurate enough for this specific case.
I hope this clarifies how to find the normal approximation for the given binomial probability and compare it to Table B of the normal distribution.