all Every day, about 1,072 customers are served per restaurant, per day. or appr

Question

all Every day, about 1,072 customers are served per restaurant, per day. or approximalely 11.8 million customers daily worldwide. Mort than 2.1 billion hamburgers ara sold at Burger King restaurants annually. Assume the number customers served per day is normally distributed Suppose you learn 5% of Burger King restaurants serve at least 1,750 customers per day. What is the standard deviation of the number of customers served per day? What is the probability that a Burger king restaurant has 950 to 1,250 customers per day? The 3 percent of lowest selling Burger King Restaurants sell to how many customers per day?

Explanation / Answer

P( X > 1750 ) = 0.05

P ( X < 1750) = 0.95

Writing in the standard normal form, mean = 1072

Thus,

P ( Z < 1750 - 1072 / sd ) = 0.95

Taking inverse, we have:

678 / sd = F-1 (0.95) = 1.65

SD = 678 / 1.65

= 411 customers are the standard deviation.

b) P ( 950 < X < 1250)

= P ( -0.30 < Z < 0.43)

= 0.6664 - 0.3821

= 0.2843

= 28.43% is the probability of serving 950 to 1250 customers per day

c) Lowest 3% selling burger king:

P ( X - 1072 / 411) = 0.03

Taking inverse probability

X - 1072 / 411 = -1.88

X = 1072 - (1.88 * 411)

= 299.32

~ 300 customers per day

Hope this helps.

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