Ajournal published a study of the lifestyles of visually impaired students. using diaries, the students kept track of several variables, including number of hours of sleep obtained in a typical day. these visually impaired students had a mean of 8.89 hours and a standard deviation of 2.11 hours. assume that the distribution of the number of hours of sleep for this group of students is approximately normal. complete parts a through c.

a. find p(x < 6). p(x < 6) = (round to four decimal places as needed.)
b. find p(8 lessthanorequalto x lessthanorequalto 10) p(8 lessthanorequalto x lessthanorequalto 10) = (round to four decimal places as needed.)
c. find the value a for which p(x < a) = 0.2. (round to two decimal places as needed.)

a)

b)

c)

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent interest on this case, and for this case we know the distribution for X is given by:

And let represent the sample mean, the distribution for the sample mean is given by:

a. Find P(x < 6). P(x < 6) = (Round to four decimal places as needed.)

In order to find this probability we can use the z score given by this formula

And if we use this we got this:

b. Find P(8 < x < 10)  = (Round to four decimal places as needed.)

c. Find the value a for which P(x < a) = 0.2. (Round to two decimal places as needed.)

For this case we can use the definition of z score given by:

First we need to find a z score that accumulates 0.2 of the area on the left tail, and the z score on this case is z=-0.842. and using this z score we can solve for x like this:

And if we solve for x we got:

And that would be the value required for this case.

6 (3) - 4 + 32

hope this

stew reads at the fastest rate of 265 words per minute.

step-by-step explanation:

it's a given that felicia reads at 260 word per minute and on connie's graph we can see that she reads 200 words per minute. since stew's table tells us that he read 795 in 3 minutes, we can divide 795 by 3 to find out how many words he reads per minute.

795/3 = 265

stew reads 265 words per minute - he reads at the fastest rate since felecia reads at 260 words per minute and connie reads at 200 words per minute.

stew (265) > felecia (260) > connie (200)