Compute​ P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If​ so, approximate​ P(X) using the normal distribution and compare the result with the exact probability.   n=40​, p=0.3​, and X=15 ​P(X)=nothing ​(Round to four decimal places as​ needed.) Can the normal distribution be used to approximate this​ probability?     A. ​No, the normal distribution cannot be used because ​np(1−​p)<10.   B. ​No, the normal distribution cannot be used because ​np(1−​p)≥10.   C. ​Yes, the normal distribution can be used because ​np(1−​p)<10.   D. ​Yes, the normal distribution can be used because ​np(1−​p)≥10. Approximate​ P(X) using the normal distribution. Use a standard normal distribution table. Select the correct choice below and fill in any answer boxes in your choice.     A. ​P(X)=nothing ​(Round to four decimal places as​ needed.)   B. There is no solution. By how much do the exact and approximated probabilities​ differ? Select the correct choice below and fill in any answer boxes in your choice.     A. nothing ​(Round to four decimal places as​ needed.)   B. There is no solution.

Assume the random variable x is normally distributed with mean μ=81 and standard deviation σ=4. Find the indicated probability. P(71<X<74)=____________. (round answer to four decimal places.)

Find the probability using the normal distribution. Use a TI-83 Plus/TI-84 Plus calculator and round the answer to at least four decimal places. P(z<-2.64) = ||

Compute P(x) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(x) using the normal distribution and compare the result with the exact probability. n = 68, p = 0.71, and x = 53 Approximate P(x) using the normal distribution. Select the correct choice below and fill in any answer boxes in your choice. OA. P(x)= (Round to four decimal places as needed.) B. The normal distribution cannot be used to approximate the binomial distribution in this case. Compare the normal approximation with the exact probability. Select the correct choice below and fill in any answer boxes in your choice. OA. The exact probability is greater than the approximated probability by (Round to four decimal places as needed.) B. The exact probability is less than the approximated probability by (Round to four decimal places as needed.) OC. The exact and approximated probabilities are equal. O D. The normal distribution…