Apply the Distributive property to the expression 4(3x +5y - 4) to produce an equivalent expression.

A machine is used to fill Apple Juice bottles with juice. The machine has a known standard deviation of σ = 0.05 liters. The tar

Lina20 [59]

Answer:

The probability that the quality control manager will shut down the machine is 0.0002.

Step-by-step explanation:

We are given that a machine is used to fill Apple Juice bottles with juice. The machine has a known standard deviation of σ = 0.05 liters. The target mean fill volume is µ = 2.0 liters.

A quality control manager obtains a random sample of 50 bottles. He will shut down the machine if the sample of these 50 bottles is less than 1.95 or greater than 2.1.

Let $\bar X$ = sample mean fill volume

The z score probability distribution for sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean fill volume = 2 liters

$\sigma$ = standard deviation = 0.05 liters

n = sample of bottles = 50

Now, it is provided that he will shut down the machine if the sample of these 50 bottles is less than 1.95 or greater than 2.1.

So, Probability that the sample of these 50 bottles is less than 1.95 is given by = P( $\bar X$ < 1.95)

P( $\bar X$ < 1.95) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{1.95-2}{\frac{0.05}{\sqrt{50} } }$ ) = P(Z < -7.07) = 1 - P(Z $\leq$ 7.07)