Question

Toothpaste Ken is traveling for his business. He has a new 0.85-ounce tube of toothpaste that’s supposed to last him the whole trip. The amount of toothpaste Ken squeezes out of the tube each time he brushes varies according to a Normal distribution with mean 0.13 ounces and standard deviation 0.02 ounces. If Ken brushes his teeth six times on a randomly selected trip, what’s the probability that he’ll use all the toothpaste in the tube?

Answer 1

Using the normal distribution, it is found that there is a 0.2798 = 27.98% probability that he’ll use all the toothpaste in the tube.

In a normal distribution with mean $\mu$ and standard deviation $\sigma$, the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

• It measures how many standard deviations the measure is from the mean.  
• After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
• When a variable is multiplied by a constant, both the mean and the standard deviation are multiplied by the constant.

In this problem:

• Brushes 6 times.

• Each time, mean of 0.13 ounces, hence, for the 6 times, $\mu = 0.13(6) = 0.78$
• Each time, standard deviation of 0.02 ounces, hence, for the 6 times, $\sigma = 0.02(6) = 0.12$.

The probability that he’ll use all the toothpaste in the tube is 1 subtracted by the p-value of Z when X = 0.85, hence:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{0.85 - 0.78}{0.12}$

$Z = 0.583$

$Z = 0.583$ has a p-value of 0.7202.

1 - 0.7202 = 0.2798

0.2798 = 27.98% probability that he’ll use all the toothpaste in the tube.

A similar problem is given at https://brainly.com/question/24663213