Question

Check my work Check My Work button is not enabled 1 Item 3 Item 3 10 points Beer bottles are filled so that they contain an average of 445 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 7 ml. a. What is the probability that a randomly selected bottle will have less than 440 ml of beer

Answer 1

Answer: The probability that a random selected bottle will have less than 440 ml of beer is 23.882% (0.23882)

find attached drawing of the area under the normal distribution and readings off the normal distribution table

Step-by-step explanation:

QUESTION: Beer bottles are filled so that they contain an average of 445 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 7 ml. a. What is the probability that a randomly selected bottle will have less than 440 ml of beer

ANSWER:

Taken the given data from the question,

mean = μ = 445 ml

standard deviation = σ = 7 ml

x= 440 ml

One would also need to illustrate the area covered by such a region in a normal distribution curve (Kindly find attached a diagram of this)

FIRST STEP Find the z-score

The distribution is a normal distribution, so the z-score is

z = (x-μ)/σ = (440 - 445)/7 = -0.71 (2 d.p)

SECOND STEP Finding the probability of the z-score from a normal distribution which is equivalent to the the probability we are looking for

Pr(x < 440 ml) = Pr (z < -0.71) = 0.23882 [THIS IS GOTTEN FROM THE STANDARD NORMAL DISTRIBUTION TABLE, kindly find attached a picture illustrating the way the solution is gotten from the table]

The standard normal distribution table takes the probability of areas to the left. Reading the table one should take the the value with -0.7 and the 0.01.

Therefore, the probability of a beer chosen at random to be less than 440 ml is 23.882% (leaving in percentage or 0.23882)