Question

At the farmers market a farmer has bunches of radishes for sale. The

weight of the radish bunches is normally distributed with a mean of
6 ounces and a standard deviation of 0.5 ounces. What is the
probability a random selected radish bunch weighs between 5 and
6.5 ounces?

Answer 1

The probability a random selected radish bunch weighs between 5 and 6.5 ounces is 0.8185

Explanation:

The weight of the radish bunches is normally distributed with a mean of 6 ounces and a standard deviation of 0.5 ounces

Mean =
`\mu = 6`

Standard deviation =
`\sigma = 0.5`

We are supposed to find the probability a random selected radish bunch weighs between 5 and 6.5 ounces i.e.P(5<x<6.5)

`Z=(x-\mu)/(\sigma)`

At x = 5

`Z=(5-6)/(0.5)`

Z=-2

`Z=(x-\mu)/(\sigma)`

At x = 6.5

`Z=(6.5-6)/(0.5)`

Z=1

Refer the z table for p value

P(5<x<6.5)=P(x<6.5)-P(x<5)=P(Z<1)-P(Z<-2)=0.8413-0.0228=0.8185

Hence the probability a random selected radish bunch weighs between 5 and 6.5 ounces is 0.8185