3. A website, hugeretail.com, features a huge variety of products for upscale co

Question

3. A website, hugeretail.com, features a huge variety of products for upscale consumers. These consumers are segmented into "mobile" and "desktop" consumers, as a function of how they complete the majority of their purchases, either via phone or some other device such as a laptop, 38% of the site's consumer base are mobile consumers. The Consumer Fraud Division of the Department of Justice has begun a preliminary investigation into the online practices of hugeretail.com after an article exposed complaints of padded charges. Their first task is to choose a random sample of 20 customers for interviews and data collection regarding their transactions with hugeretail.com. What is the probability that 8 of the 20 randomly chosen consumers will be mobile consumers? What is the probability that between 12 and 14 of the 20 randomly chosen consumers will be desktop consumers? . What is the probability that 3 or fewer of the randomly chosen consumers will be desktop consumers?

Explanation / Answer

Probability that 8 of the 20 randomly chosen consumers are mobile consumers

= 20C8 * 0.388 * 0.6212

= 125970 * 0.0000014

= 0.1764.

For desktop consumers

p = 0.62 n = 20

Mean = np = 0.62 * 20 = 12.4

Standard deviation = (np(1-p))

= (12.4*0.38)

= 4.712

X = 11.5

Z = (11.5 - 12.4) / 4.712 = -0.1910

Probability from tables = 0.4243

X = 14.5

Z = (14.5 - 12.4) / 4.712 = 0.4457

Probability from tables = 0.6721

=> Probability that between 12 and 14 will be mobile consumers = 0.6721 - 0.4243 = 0.2478.

X = 3.5

Z = (3.5 - 12.4) / 4.712 = -1.889

Probability from tables = 0.0294.

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