Answer:
Probability that a randomly selected can will have less than 15.5 ounces is 0.1587.
Step-by-step explanation:
We are given that the amount of soda in a 16-ounce can is normally distributed with a mean of 16 ounces and a standard deviation of 0.5 ounce.
<em>Let X = amount of soda</em>
So, X ~ N()
The z-score probability distribution for normal distribution is given by;
Z = ~ N(0,1)
where, = mean amount = 16 ounces
= standard deviation = 0.5 ounce
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, the probability that a randomly selected can will have less than 15.5 ounces is given by = P(X < 15.5 ounces)
P(X < 15.5 ounces) = P( <
) = P(Z < -1) = 1 - P(Z
1)
= 1 - 0.8413 = 0.1587
<em>Now, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1 in the z table which has an area of 0.8413.</em>
Hence, the probability that a randomly selected can will have less than 15.5 ounces is 0.1587.