Miguel buys a large bottle and a small bottle of juice. The amount of juice that the manufacturer puts in the large bottle is a random variable with a mean of 1016 ml and a standard deviation of 8 ml. The amount of juice that the manufacturer puts in the small bottle is a random variable with a mean of 510 ml and a standard deviation of 5ml. If the total amount of juice in the two bottles can be described by a normal model, what's the probability that the total amount of juice in the two bottles is more than 1540.2 ml?

Pr (X>1540.2) = 0.0655

Step-by-step explanation:

Expected value of large bottle,

E (Large) = 1016

Expected value of small bottle,

E (small) = 510

Expected value of total

E (total) = 1016 + 510 = 1526

So the new mean is 1526

Find standard deviation of new amount by variance

Variance of large bottle,

v (large) = 8^2 = 64

Variance of small bottle,

v (small) = 5^2 = 25

Variance of total

v (total) = 64+25 = 89

So the new standard deviation

sd (new) = sqrt (89) = 9.434

Find probability using the new mean and s. d.

Pr (X>1540.2)

Z score, z = (x-mean) / sd

= (1540.2 - 1526) / 9.434

= 1.505

value in z score

P (z<1.51) = 0.9345

For probability of x > 1540.2

P (z > 1.51) = 1 - 0.9345 = 0.0655