Let X denote the number of VCRS sold during a random week by a certain store. The probability function of X is x f(x) 0 0.6164 1 0.0956 2 0.0354 3 0.0461 4 0.2065 a) Calculate the expected number of VCRs sold in a random week. E[X] = 1.2307 x b) Calculate E[4X + 2] = 6.9228 X

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=56  p=0.5   x=30  A)For n=56​, p=0.5​, and X=30, use the binomial probability formula to find​ P(X).     B)Can the normal distribution be used to approximate this​ probability? A. ​No, because np(1−p)≤10   B. ​Yes, because np(1−p)≥10   C. ​Yes, because np(1−p)≥10   D. ​No, because np(1−p)≤10   C) Approximate​ P(X) using the normal distribution. Use a standard normal distribution table. A. ​P(X)=enter your response here ​(Round to four decimal places as​ needed.)   B. The normal distribution cannot be used.     D) By how much do the exact and approximated probabilities​ differ? A.enter your response here ​(Round to four decimal places as​ needed.) B. The normal distribution cannot be used.   E)By…