Question

The waking time of a student under common conditions is normally distributed with mean of 30 hours and a standard deviation of 5 hours. What value of waking hours is exceeded with 95% probability?

Answer 1

Answer:

If the walking time is greater than or equal to 38.225 hours, than it exceeds 95% probability that is lie in top 5%.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 30 hours

Standard Deviation, σ = 5 hours

We are given that the distribution of waking time is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to find the value of x such that the probability is 0.95

$P( X < x) = P( z < \displaystyle\frac{x - 30}{5})=0.95$  

Calculation the value from standard normal z table, we have,  

$\displaystyle\frac{x - 30}{5} = 1.645\\\\x = 38.225$  

Thus, if the walking time is greater than or equal to 38.225 hours, than it exceeds 95% probability that is lie in top 5%.