6. Students in the psychology department consume an average of 5 cups of coffee

Question

6. Students in the psychology department consume an average of 5 cups of coffee per day with a standard deviation of 1.75 cups. The number of cups of coffee consumed is normally distributed What proportion of students consumes an amount equal to or less than 6 cups per day? How many cups would an individual at the 80th percentile drink? 7. In a recent study, it was found that the correlation between self-esteem and depression was -0.64. Explain what this means. Calculate the coefficient of determination for this correlation and explain what information thi provides. 8. In a recent study, it was found that the correlation between self-esteem and depression was-0.64. Tom interprets this to mean that low levels of self-esteem lead to high levels of depression and vice versa. How is Tom misinterpreting these data?

Explanation / Answer

6) MEAN= 5 AND STANDARD DEVIATION IS 1.75 CUPS

Proportion of students consumes an amount equal to or less than 6 cups per day is

Since =5 and =1.75 we have:

P ( X<6 )=P ( X<65 )=P ((X)/<(65)/1.75)

Since (x)/=Z and (65)/1.75=0.57 we have:

P (X<6)=P (Z<0.57)

Use the standard normal table to conclude that:

P (Z<0.57)=0.7157

So 0.7157 or 71.57% students consumes an amount equal to or less than 6 cups per day.

b) Firstly convert 80th percentile that 0.8 into z score by using normal table .

Z= 0.84

Z=X-MU/SIGMA

0.84= X-5/1.75

0.84*1.75= X-5

1.47=X-5

X= 5+1.47= 6.47 = 6.5 = 6 cups(approx)

7) r= -0.64 which is negative correlation which means low self esteem leads to depression. Lower the self esteem will leads to more in depression. Or we can also say higher the depression lower the self esteem.

Coefficient of determination is r sqarred = (-0.64)^2= 0.4096 indicates that the model explains 40.96% of the variability of the response data around its mean.

I have answered the first two. Please Repost question 8 . Thank you!

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