Q1) 4 machines manufacture cylindrical steel pins. Pins are subject to diameter specification. A pin may meet specification, or it may be too thin or too thick. Pins are arbitrarily sampled from each machine, and number of pins in each category is counted. Following table presents results. Is proportion of pins which are too thin, OK, or too thick is same for all machines?
|
|
Too Thin
|
OK
|
Too Thick
|
|
Machine 1
|
10
|
102
|
8
|
|
Machine 2
|
34
|
161
|
5
|
|
Machine 3
|
12
|
79
|
9
|
|
Machine 4
|
10
|
60
|
10
|
Pizza
Leo has pizza business. Times to create and deliver pizzas are approximately normally distributed with mean m =20 minutes and standard deviation s = 10 minutes.
Assume that Leo advertises "If it takes more than 30 minutes to get your pizza, you get it free". What percentage of his take-out pizzas will have to give away free?
How long a time must Leo allow if he wishes to give away no more than 5% of pizzas?