If x is a binomial variable with p = .4 and n = 25, write the probability that you would be looking for after you have applied the continuity correction factor for the following conditions for x:
3) x = 5
4) x > 5
5) x ≤ 5
Continuity Correction Factor:
You add or subtract .5, depending on the condition.
3) P(4.5 < x < 5.5) for x = 5
4) P(x > 5.5) for x > 5
5) P(x < 5.5) for x ≤ 5
To calculate the probability for given conditions after applying the continuity correction factor, we need to convert the discrete binomial distribution to a continuous distribution by subtracting or adding 0.5 to the values. Here are the calculations for each condition:
3) x = 5:
To apply the continuity correction factor, we subtract 0.5 from each boundary of x. So, the probability you would be looking for is the probability that x falls between 4.5 and 5.5. We can calculate this using the cumulative distribution function (CDF) of the binomial distribution. Let's denote it by P(X).
P(X = 5) = P(4.5 ≤ X ≤ 5.5)
= P(X ≤ 5.5) - P(X ≤ 4.5)
= P(X ≤ 6) - P(X ≤ 5)
To find these probabilities, we can use a binomial probability table, a statistical software, or an online calculator.
4) x > 5:
To apply the continuity correction factor, we subtract 0.5 from the lower boundary of x and add 0.5 to the upper boundary. So, the probability you would be looking for is the probability that x is greater than 5.5.
P(X > 5) = 1 - P(X ≤ 5.5)
= 1 - P(X ≤ 6)
We can use the binomial probability table, a statistical software, or an online calculator to find the value.
5) x ≤ 5:
To apply the continuity correction factor, we subtract 0.5 from the upper boundary of x. So, the probability you would be looking for is the probability that x is less than or equal to 4.5.
P(X ≤ 5) = P(X ≤ 4.5)
Again, you can use a binomial probability table, a statistical software, or an online calculator to find the value.