1. (6) A student studying the sleeping habits of seniors at...

1. (6) A student studying the sleeping habits of seniors at his school asked 10 randomly- selected seniors how many hours of sleep they got the previous night. The data, rounded to the nearest half-hour, is given in the table below. 8 7.5 9 7.5 9 6 5 9 7.5 7 a. (3) Use your stapplet or a calculator to find the mean and standard deviation of these data. b. (3) Determine if there are any outliers in these data. Show your work.

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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