Question

If np 25 and ng≥5, estimate Pifewer than 8) with n=14 and p=0.6 by using the normal distribution as an approximation to the binomial distribution: if np <5 or ng <5, then state that the normal approximation is not suitable Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. P(fewer than 8)= (Round to four decimal places as needed) OB. The normal approximation is not suitable

Answer 1

In order to estimate P(fewer than 8) with n = 14 and p = 0.6 using the normal distribution as an approximation to the binomial distribution, the conditions np > 5 and n(1-p) > 5 need to be satisfied. In this case, we can use the normal distribution as an approximation. The estimated value of P(fewer than 8) is 0.3758.

Step-by-step explanation:

In order to estimate P(fewer than 8) with n = 14 and p = 0.6 using the normal distribution as an approximation to the binomial distribution, we need to check if np and n(1-p) are both greater than 5.

In this case, np = 14 * 0.6 = 8.4 and n(1-p) = 14 * 0.4 = 5.6, so both conditions are satisfied.

We can use the normal distribution as an approximation to the binomial distribution.

The mean (μ) is equal to np = 8.4 and the standard deviation (σ) is equal to √(np(1-p)) = √(8.4 * 0.4) = 1.63299.

To estimate P(fewer than 8), we need to calculate the z-score for x = 8. To do this, we subtract 0.5 from x, giving us z = (8 - 0.5 - μ) / σ = (8 - 0.5 - 8.4) / 1.63299 = -0.3206.

Using a standard normal distribution table or calculator, we can find the area to the left of z = -0.3206, which is approximately 0.3758.

Therefore, the estimated value of P(fewer than 8) is 0.3758.