Question

The amount dispensed by a soft-drink dispensing machine has a normal distribution with mean μ and standard deviation 0.155 ounce. The mean amount dispensed, μ , can be controlled. At what value should μ be set so that a 16 ounce cup will overflow with probability 0.01? Round your answer to two decimal places.

Answer 1

Answer:
`\mu=15.64`

Explanation:

Let x be a random variable that represent the amount dispensed by a soft-drink dispensing machine which has a normal distribution with mean μ and standard deviation
`\sigma=` 0.155 ounce.

To find : μ such that P(X>16)=0.01

Consider P(X>16)=0.01

`P((X-\mu)/(\sigma)>(16-\mu)/(0.155))=0.01`

Since,
`Z=(X-\mu)/(\sigma)`

Also, z-table , one -tailed z-value for p-value of 0.01= 2.326

Then,
`(16-\mu)/(0.155)=2.326`

`\Rightarrow {16-\mu}=0.155*2.326\\\\\Rightarrow {16-\mu}=0.36053\\\\\Rightarrow\ \mu=16-0.36053=15.63947\approx15.64\\\\\Rightarrow\ \mu=15.64`