3. Christmas Spending. In a recent study done by the National Retail Federation

Question

3. Christmas Spending. In a recent study done by the National Retail Federation found that 2017 Christmas spending for all US households follow a Normal distribution with mean $950 and a standard deviation $60. Use this information to answer the following questions. (a) What is the probability that 2017 Christmas spending for a US household is greater than $930? Answer this question by completing parts 3(a)i and 3(a)i i. Provide the z-score corresponding to the 2017 Christmas spending of $930. ii. Based on your answer in 3(a)i, what is the probability of 2017 Christmas spending for a US household is greater than S930? (b) Free response submission. Provide the z-score corresponding to the 2017 Christmas spending of $1200, and the probability of 2017 Christmas spending for a US household is more than $1200. (c)Find Q1 (First Quartile). Answer this question by completing parts 3(c)i. and 3(c)ii. i. Provide the z-score corresponding to Q1 ii. Based on your answer in 3(c)i, provide the value of Q1. (d) Find Qs (Third Quartile). Answer this question by completing parts 3(d)i and 3(d)ii. i. Provide the z-score corresponding to Qs ii. Based on your answer in 3(d)i, provide the value of Qs households? context of the problem (e) What is the value of the IQR for the distribution of 2017 Christmas spending for all US (f) Free response submission. Interpret the value of the IQR from question 3e within the

Explanation / Answer

Question 3

Mean chirstmas spending = $ 950

Standard deviation christmas spending = $ 60

(a) Here the Z - score = (930 - 950)/60 = -0.3333

(ii) Pr(Spending > $ 930 ; $ 950 ; $ 60) = 1 - Pr(Z < -0.3333) = 1- 0.3695 = 0.6305

(b) Z score = (1200 - 950)/60 = 4.1667

Pr(Spending > $ 1200 ; $ 950 ; $ 60) = 1 - Pr(Z < 4.1667) = 1- 0.9999 = 0.000001

(c) Here Q1  means 25 percentile. So, here as per z - table

then,

Pr(X < Q1 ; $ 950 ; $ 60) = 0.25

Z - score = NORMSINV(0.25)= -0.6745

Q1 - 950 = 60 * (- 0.6745)

Q1 = 950 - 60 * 0.6745 = $ 909.53

(d) For Q3 ; the percentile value is 0.75 . as normal dsribution is symetric.

The Z - value = 0.6745

Q3 = 950 + 0.6745 * 60 = $ 990.47

(e) IQR = Q3 - Q1 = 990.47 - 909.53 = $ 80.94

(f) Here IQR can be seen here as the 50% of households in US spend in between the spanof $ 80.94

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