Respuesta :
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- 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, [tex]\mu = 0.13(6) = 0.78[/tex]
- Each time, standard deviation of 0.02 ounces, hence, for the 6 times, [tex]\sigma = 0.02(6) = 0.12[/tex].
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:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.85 - 0.78}{0.12}[/tex]
[tex]Z = 0.583[/tex]
[tex]Z = 0.583[/tex] 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
