Answer :
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:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to find the value of x such that the probability is 0.95
[tex]P( X < x) = P( z < \displaystyle\frac{x - 30}{5})=0.95[/tex]
Calculation the value from standard normal z table, we have,
[tex]\displaystyle\frac{x - 30}{5} = 1.645\\\\x = 38.225[/tex]
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%.