Question

(1 point) The manager of Walton's Discount Shoe Store knows that daily revenue from shoe sales is normally distributed with mean $ 3500 and standard deviation $ 800. Find the probability (to four decimal places) that
(a) on a particular day, revenue exceeds $ 4200.

(b) on three consecutive days, revenue never exceeds $ 3500.

(c) on four consecutive days, the average revenue exceeds $ 4300.

Answer 1

Solution :

(a)

P(x > 4200) = 1 - P(x < 4200)

= 1 - P[(x - $\mu$ ) / $\sigma$ < (4200 - 3500) / 800)

= 1 - P(z < 0.875)

= 1 - 0.8092

= 0.1908

Probability = 0.1908

(b)

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 800 / $\sqrt$ 3 = 461.8802

P($\bar x$ > 3500) = 1 - P($\bar x$ < 3500)

= 1 - P[($\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ _{$\bar x$} < (3500 - 3500) / 461.8802]

= 1 - P(z < 0)

= 1 - 0.5

= 0.5

Probability = 0.5

(c)

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 800 / $\sqrt$ 4 = 400

P($\bar x$ > 4300) = 1 - P($\bar x$ < 4300)

= 1 - P[($\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ _{$\bar x$} < (4300 - 3500) / 400]

= 1 - P(z < 2)

= 1 - 0.9772

= 0.0228

Probability = 0.0228