or
x = sz + mOn Friday we began to tackle questions such as "what percentage of customers arrive by 6:45?" "If total customers = 60, how many by 7:15?" and other questions.
If the underlying distribution is normal (or at least "heaped" or "round" shaped), then we can convert our x values to z values if we know the m and r, and then use the standard normal curve.
Processes: x ® z ® % or % ® z ® x
z = or
x = sz + m
What is the probability a Kalanchoe leaf will be 18 cm or shorter given m=1.7.1 cm, s = 0.9cm
m = 17.1 cm
s = 0.9 cm
z = (18 - 17.1)/0.9 = 1
0.9
Look up z value 1.00 from table 5 on page A7
= 0.3413 should go familiar, eh, but probality is not just 34%
It is 34% plus 50%
= 0.8413
Next example:
Dominos pizza knows that the average length of time from receiving an order to delivering to the customer is 20 minutes with a standard direction 7 min. 45 seconds. Treat there statistics as population parameters for now. Dominos wants to guarantee a delivery time as part of a marketing campaign, "Your pizza in ____ minutes or your money back! Dominos is willing to refund 10% of their orders, what is the quickest delivery time they should set the guarantee at?
m = 20
z = 7.75
10% will be late & customers guarantees will get a refund. This time makes few very loyal customers!
Thus we "want" 10% of the pizzas to arrive late, so to speak. Or we want 90% to be on time. This is a % ® z ® x problem. But we cannot look up 90% in the table: the 90% is from negative infinity to positive infinity. The distance 0 to z is 0.90 (90%) minus 0.50 or 0.40. We look that up in the table on page A7 and the closest we can get to 0.40 is 0.3997 or a z of 1.28.
Using x = sz + m we can determine x to be: x = (7.75)(1.28) +20 = 29.92 minutes
So you guarantee delivery in 30 minutes or less and you’ll only pay out on 10% of the pizzas. (From the perpective of Domino's this is a "Buy ten get one free" type of deal.).
In class p304 2,20,(22abcd)
Homework p304-307 1,3,5,11,19,23