For a 4-unit class like Statistics, students should spend average of 12 hours studying for the class. A survey was done on 22 students, and the distribution of total study hours per week is bell-shaped with a mean of 12 hours and a standard deviation of 3.4 hours. Use the Empirical Rule to answer the following questions. a) 68% of the students spend between hours andb) 95% of the students spend between hours andc) 99.7% of the students spend between hours and hours on Statistics each week. hours on Statistics each week. hours on Statistics each week.

 a) About 68% of the students spend between 8.6 hours and 15.4 hours .

b) About 95% of the students spend between 5.2 hours and 18.8 hours .

c) About 99.7% of the students spend between 1.8 hours and 22.2 hours .

Step-by-step explanation:

The famous Empirical rule states that ;

Since , the distribution of total study hours per week is bell-shaped that means it follows normal distribution.

Mean = 12 hours

Standard deviation: 3.4 hours

Now ,

a) Mean± Standard deviation = 12 ± 3.4  hours

= (12-3.4, 12+3.4)  hours

= ( 8.6 , 15.4) hours

∴About 68% of the students spend between 8.6 hours and 15.4 hours .

b) Mean± 2 Standard deviation = 12 ± 2(3.4) hours

= 12 ± 6.8 hours

= (12-6.8, 12+6.8)  hours

= ( 5.2 ,18.8) hours

∴About 95% of the students spend between 5.2 hours and 18.8 hours .

c) Mean± 3 Standard deviation = 12 ± 3(3.4) hours

= 12 ± 10.2 hours

= (12-10.2, 12+10.2)  hours

= ( 1.8 ,22.2) hours

∴About 99.7% of the students spend between 1.8 hours and 22.2 hours .

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

step-by-step explanation:

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