Question

A.) Suppose that the average time spent sleeping (in hours) for a group of medical residents at a hospital can be approximated by a normal distribution with mean 6.1 and standard deviation 1.0. The middle 50% of patients sleep between 5.42 hours and what other length of time? Answers should be correct to two decimal places. B.) Suppose that the average time spent sleeping (in hours) for a group of medical residents at a hospital can be approximated by a normal distribution with mean 6.1 and standard deviation 1.0. What is the shortest time spent sleeping that would still place a resident in the top 5% of sleeping times? Answers should be correct to two decimal places C.) Suppose that the average time spent sleeping (in hours) for a group of medical residents at a hospital can be approximated by a normal distribution with mean 6.1 and standard deviation 1.0. What sleeping time is the 58th percentile? Answers should be correct to two decimal places.

          A.) Suppose that the average time spent sleeping (in
hours) for a group of medical residents at a hospital can be
approximated by a normal distribution with mean 6.1 and
standard deviation 1.0.  The middle 50% of patients
sleep between 5.42 hours and what other length of time?
Answers should be correct to two decimal
places.
B.) Suppose that the average time spent sleeping (in
hours) for a group of medical residents at a hospital can be
approximated by a normal distribution with mean 6.1 and
standard deviation 1.0.  What is the shortest time spent
sleeping that would still place a resident in the top 5% of
sleeping times? Answers should be correct to two decimal
places
C.)  Suppose that the average time
spent sleeping (in hours) for a group of medical residents at
a hospital can be approximated by a normal distribution with mean
6.1 and standard deviation 1.0.  What sleeping time
is the 58th percentile? Answers should be correct to two
decimal places.

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Added by Courtney V.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Shaiju T

04/14/2022

Step 1

42 hours and what other length of time, we first calculate the critical scores for the left and right sides. Given: Mean (μ) = 6.1 Standard Deviation (σ) = 1.0 Left critical score (Zα/2) = -0.6745 Right critical score (Zα/2) = 0.6745 Show more…

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A.) Suppose that the average time spent sleeping (in hours) for a group of medical residents at a hospital can be approximated by a normal distribution with mean 6.1 and standard deviation 1.0. The middle 50% of patients sleep between 5.42 hours and what other length of time? Answers should be correct to two decimal places. B.) Suppose that the average time spent sleeping (in hours) for a group of medical residents at a hospital can be approximated by a normal distribution with mean 6.1 and standard deviation 1.0. What is the shortest time spent sleeping that would still place a resident in the top 5% of sleeping times? Answers should be correct to two decimal places C.) Suppose that the average time spent sleeping (in hours) for a group of medical residents at a hospital can be approximated by a normal distribution with mean 6.1 and standard deviation 1.0. What sleeping time is the 58th percentile? Answers should be correct to two decimal places.

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Transcript

00:01 Hey everyone in this question we are given the values of mu and sigma and we need to find out the middle 50 % of the time middle 50 % is represented by middle 0 .5 area about mean it implies that 0 .5 over 2 is equal to 0 .25 is the area on the left side and 0 .25 is the right side of mean so the value of mu is 6 .1 and sigma is 1 and the value corresponding to alpha is equal to 0 .25 for the left tailed is z alpha which is equal to minus 0 .6745 and right tailed is z alpha is equal to 0 .675.

00:39 Okay.

00:40 So here the left 25 % area is given by the left 25 % area is given by z is equal to x minus mu over sigma.

00:52 So here the value of j is minus 0 .675 is equal to x minus 6 .1 over sigma is 1 where x is the sleeping time mu is mean and sigma is standard deviation and z is the left 25 % critical score so x is equal to we simplify this and this is equal to 5 .4285 okay so this is the value of x now the 9 25 % r is z is equal to x minus mu over sigma where x is the sleeping time z is the critical right score okay so this is equal to 0 .675 is equal to 0 .6 .75 is equal to conducts minus 6 .1 over 1 so here we have the value we simplify this and x is equal to 6 .77 okay so the other length time of middle 50 % of sleep is 6 .77 hours okay hence the middle 50 % is between 5 .42 and 6 .77 hours so this is the answer of a part now in the b part we have the top 5 % the top 5 % is represented by is represented by 0 .5 area okay so this is the graph of 5 % area so this is the graph of 5 % area and this is 0 .95 so this is the top 5 % area now here alpha is equal to 0 .05 and z value corresponding to alpha is equal 0 .05 and right tailed that is alpha by 2 is equal to 1 .6449 okay so here we use the formula of z is equal to x minus mu or sigma so x is equal to mu plus z alpha so x is equal to 6 .1 plus 1 .6449 multiply 1 so here we have the value of x is equals to 7 .74 so the shortest time spent sleeping that would place a resident in to 5 % of sleeping is 7 .744 or so the shortest time...

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