the amount of daily time that teenagers spend on a brand a cell phone is normally distributed with a given…

the amount of daily time that teenagers spend on a brand a cell phone is normally distributed with a given mean μ = 2.5 hr and standard deviation σ = 0.6 hr. what percentage of the teenagers spend more than 3.1 hr? 5% 10% 16% 32%

the amount of daily time that teenagers spend on a brand a cell phone is normally distributed with a given mean μ = 2.5 hr and standard deviation σ = 0.6 hr. what percentage of the teenagers spend more than 3.1 hr? 5% 10% 16% 32%

Answer

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 3.1$, $\mu=2.5$ and $\sigma = 0.6$. So $z=\frac{3.1 - 2.5}{0.6}=\frac{0.6}{0.6}=1$.

Step2: Find the proportion in the standard normal table

The standard - normal table gives the proportion of values to the left of a given z - score. For $z = 1$, the proportion of values to the left is $0.8413$.

Step3: Calculate the proportion to the right

We want the proportion of values greater than $x = 3.1$, which is the proportion to the right of $z = 1$. Since the total area under the normal curve is 1, the proportion to the right is $1-0.8413 = 0.1587\approx16%$.

Answer:

16%