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

Question

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

What is the proportion of 2017 Christmas spending within 1.30 standard deviations from the mean? Answer this question by completing parts 3(g)i. through 3(g)iii.

i. Provide the SMALLER z-score corresponding to the above statement.

ii. Provide the LARGER z-score corresponding to the above statement.

iii. Based on your answers in 3(g)i and 3(g)ii, what proportion of 2017 Christmas spending is within 1.30 standard deviations from the mean?

Explanation / Answer

Solution:-

= 950, = 60

i) SMALLER z-score corresponding to the above statement is - 1.30.

ii) LARGER z-score corresponding to the above statement is 1.30.

iii) The proportion of 2017 Christmas spending is within 1.30 standard deviations from the mean is 0.8064.

P(- 1.30 < z < 1.30) = P(z > - 1.30) - P(z > 1.30)

P(- 1.30 < z < 1.30) = 0.9032 - 0.0968

P(- 1.30 < z < 1.30) = 0.8064

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