Question

The average time spent sleeping (in hours) for a group of medical residents at a hospital can be approximated by a normal distribution, with a mean of 6.1 hours and a standard deviation of 1.0 hours. (Source: National Institute of Occupational Safety and Health, Japan)

(a) What is the shortest time spent sleeping that would still place a resident in the top 5% of sleeping times?

(b) Between what two values does the middle 50% of the sleep times lie?

Answer 1

\\ \text{This is a normal distribution question with}
\\Mean (\mu)= 6.1
\\Standard\;Deviation (\sigma)= 1
\\\\ \text{Since we know that}
\\z_{ score } = \frac{x-\mu}{\sigma}

a) Given in the question, top 5% means p = 0.95


b) Given in the question, middle 50% means p = 0.25 to p = 0.75


&
Middle 50% values lie between 5.4255 & 6.7745