The times people smile a day follows a normal distribution
The proportion of people that smile more than 80 times a day is 15.87%
The given parameters are:
[tex]\mathbf{\mu = 62}[/tex] --- mean
[tex]\mathbf{\sigma = 18}[/tex] -- standard deviation
The proportion that smile more than 80 times, means that:
[tex]\mathbf{x = 80}[/tex]
First, we calculate the z-score
[tex]\mathbf{z = \frac{x - \mu}{\sigma}}[/tex]
So, we have:
[tex]\mathbf{z = \frac{80- 62}{18}}[/tex]
[tex]\mathbf{z = \frac{18}{18}}[/tex]
[tex]\mathbf{z = 1}[/tex]
So, the proportion is:
[tex]\mathbf{P(x > 80) = P(z > 1)}[/tex]
Using the z-table of probabilities, we have:
[tex]\mathbf{P(x > 80) = 0.15866}[/tex]
Express as percentage
[tex]\mathbf{P(x > 80) = 15.866\%}[/tex]
Approximate
[tex]\mathbf{P(x > 80) = 15.87\%}[/tex]
Hence, the proportion of people that smile more than 80 times a day is 15.87%
Read more about probabilities of normal distributions at:
https://brainly.com/question/6476990
