Question

t your supermarket, the typical shopper spends $18.93 with a standard deviation of $12.52. you are wondering what would happen in a typical morning hour with 400 typical shoppers, assuming that each one shops independently. q18. how likely it is that you will exceed $8,000 in total sales for all 400 shoppers? a) 0.043 b) 0.102 c) 0.0121 d) 0.223

Answer 1

If your supermarket, the typical shopper spends $18.93 with a standard deviation of $12.52. You will exceed $8,000 in total sales for all 400 shoppers by: a) 0.043.

What is the probability ?

The standard deviation of the total sales is:

20 * $12.52

= $250.40

The z-score can be calculated using the formula:

z = (x - μ) / σ

where:

x = value we want to find the probability for

μ= mean

σ =standard deviation

So,

x = $8,000

μ = $7,572

σ = $250.40

Plugging these values into the formula

z = ($8,000 - $7,572) / $250.40

z = 1.71

We can then use a standard normal distribution table or a calculator to find the probability associated with a z-score of 1.71.

Thus:

Probability= 0.9564

The probability of exceeding $8,000 in total sales for all 400 shoppers is:

1 - 0.9564

= 0.043

Therefore the correct option is a) 0.043.