1. According to a recent survey, 70% of all customers will return to the same gr

Question

1. According to a recent survey, 70% of all customers will return to the same grocery store. Suppose 20 customers are selected at random. a. Using the binomial probability distribution to find: i.. number of customers are expected to return to the same grocery store. ii. Variance and standard deviation of the returned customers. b. Generate an Excel output of the above probability distribution. c. According to your excel output, what is the probability that: i. exactly 10 of the customers will return? ii. all 20 will return? ii. at least 10 will return? d. Using the formula of discrete random variable to generate the mean, variance and standard deviation. You must use Excel to find your answers, and include a copy of the Excel table in your response P (x)x P(x) x-u (x-x-u P(x) Tx P(x)-

Explanation / Answer

1) a) (i) mean =np=20*0.7 =14

(ii) variance=np(1-p)=4.2

std deviation =(4.2)1/2 =2.0494

b) from excel formula binomdist(x,20,0.7,false) below are probability distribution at different x values:

c)(i) P(X=10)=0.0308

(ii)P(X=20)=0.0008

(iii)P(X>=10)=0.9829

d)

x P(x) 0 0.0000 1 0.0000 2 0.0000 3 0.0000 4 0.0000 5 0.0000 6 0.0002 7 0.0010 8 0.0039 9 0.0120 10 0.0308 11 0.0654 12 0.1144 13 0.1643 14 0.1916 15 0.1789 16 0.1304 17 0.0716 18 0.0278 19 0.0068 20 0.0008

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