A survey of Massachusetts high school students showed that the mean number of hours these students reported watching crime TV shows was 2.4 hours with standard deviation S=0.8 and that the distribution of this variable is normal. Using this information, find a. Find the z-score for a student who reported watching 2 hours of crime shows a week. b. Find the z-score for a student who reported watching 3.6 hours of crime shows a week. c. What percentage of students watch less than 3.6 hours of shows a week? d. What percentage of the sample watches between 2 hours and 3.6 hours of crime shows a week?

a)

b)

c) 93.32% of students watch less than 3.6 hours of shows a week

d) 62.57% of the sample watches between 2 hours and 3.6 hours of crime shows a week

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

a. Find the z-score for a student who reported watching 2 hours of crime shows a week.

This is Z when X = 2. So

b. Find the z-score for a student who reported watching 3.6 hours of crime shows a week

X = 3.6. So

c. What percentage of students watch less than 3.6 hours of shows a week?

pvalue of Z when X = 3.6.

has a pvalue of 0.9332

93.32% of students watch less than 3.6 hours of shows a week

d. What percentage of the sample watches between 2 hours and 3.6 hours of crime shows a week?

pvalue of Z when X = 3.6 subtracted by the pvalue of Z when X = 2.

X = 3.6

has a pvalue of 0.9332

X = 2

has a pvalue of 0.3075

0.9332 - 0.3075 = 0.6257

62.57% of the sample watches between 2 hours and 3.6 hours of crime shows a week

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.