The average time spent sleeping (in hours) for a group of medical residents at a hospital can be approximated by a normal distribution. The average is 6.1 hours with a standard deviation of 1 hour. a. What is the shortest time spent sleeping that would place a resident in the top 5% of sleeping times

7.75 hours

Step-by-step explanation:

Given that:

Mean, m = 6.1

Standard deviation, s = 1

Shortest Time spent sleeping in other to be in top 5% of sleeping time.

5% = 0.05

Zscore for P(Z > 0.05) = 1.645 (Z probability calculator)

To obtain the shortest time, x

Zscore = (x - m) / s

1.645 = (x - 6.1) / 1

1.645 = x - 6.1

1.645 + 6.1 = x

7.745 = x

x = 7.75

Sgirtws sleep time = 7.75 hours

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: