The weight of the potatoes is approximately normally distributed with population
ID: 3040719 • Letter: T
Question
The weight of the potatoes is approximately normally distributed with population mean =10 ounces and population standard deviation =1.5 ounces. Use 68-95-99.7 rule to answer the questions below:
a). What is the probability that a randomly selected potato weighs over 13 ounces?
b). What is the probability that a randomly selected potato weighs below 8.5 ounces?
c). What is the probability that a randomly selected potato weighs between 8.5 ounces and 10 ounces?
d).What is the probability that a randomly selected potato weighs between 8.5 ounces and 13 ounces?
Explanation / Answer
a) P(X > 13)
= P(z > (13 - 10)/1.5)
= P(z > 2)
= 0.025
b) P(X < 8.5)
= P(z < (8.5 - 10)/1.5)
= P(z < -1)
= 0.16
c) P(8.5 < X < 10)
= P((8.5 - 10)/1.5 < z < (10 - 10)/1.5)
= P(-1 < z < 0)
= 0.34
d) P(8.5 < X < 13)
= P((8.5 - 10)/1.5 < z < (13 - 10)/1.5)
= P(-1 < z < 2)
= 0.815
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