There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.10 cm. The second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation 0.04 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm. What is the probability that the first machine produces an acceptable cork

0.6827

Step-by-step explanation:

Given that :

Mean, μ = 3

Standard deviation, σ = 0.1

To produce an acceptable cork. :

P(2.9 < X < 3.1)

Recall :

Z = (x - μ) / σ

P(2.9 < X < 3.1) = P[((2.9 - 3) / 0.1) < Z < ((3.1 - 3) / 0.1)]

P(2.9 < X < 3.1) = P(-1 < Z < 1)

Using a normal distribution calculator, we obtain the probability to the right of the distribution :

P(2.9 < X < 3.1) = P(1 < Z < - 1) = 0.8413 - 0.1587 = 0.6827

Hence, the probability that the first machine produces an acceptable cork is 0.6827

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

a. she will receive a refund of $278.

step-by-step explanation: