Question

The weight of the potatoes is approximately normally distributed with population mean μ=10 ounces and population standard deviation σ=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?

Answer 1

Solution :

Given that,

Using Empirical rule,8.5 < X <

P($\mu$ - 1$\sigma$< X < $\mu$ + 1$\sigma$) = 68%

P($\mu$ - 2$\sigma$< X < $\mu$ + 2$\sigma$) = 95%

P($\mu$ - 3$\sigma$< X < $\mu$ + 3$\sigma$) = 99.7%

(a)

P(X > 13) = 1 - 0.975 = 0.025

(b)

P(X < 8.5) = 0.16

(c)

P(8.5 < X < 10) = P(X < 10) - P(X < 8.5) = 0.5 - 0.16 = 0.34

(d)

P(8.5 < X < 13) = P(X < 13) - P(X < 8.5) = 0.975 - 0.16 = 0.815