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: $\mu=15.64$

Step-by-step 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

$P(\dfrac{X-\mu}{\sigma}>\dfrac{16-\mu}{0.155})=0.01$

Since, $Z=\dfrac{X-\mu}{\sigma}$

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

Then, $\dfrac{16-\mu}{0.155}=2.326$

$\Rightarrow {16-\mu}=0.155\times2.326\\\\\Rightarrow {16-\mu}=0.36053\\\\\Rightarrow\ \mu=16-0.36053=15.63947\approx15.64\\\\\Rightarrow\ \mu=15.64$