The amount of soda in a 16-ounce can is normally distributed with a mean of 16 ounces and a standard deviation of .5 ounce. What is the probability that a randomly selected can will have less than 15.5 ounces? Round your answers to four decimal places.

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.

Let X = amount of soda

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

Now, in the z table the P(Z 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.

Hence, the probability that a randomly selected can will have less than 15.5 ounces is 0.1587.

the correct answer is b) histograms can be used to exhibit the shape of distributions. this is because histograms count the frequency of each possible answer, so one is able to see which results are more common and which are less common.