A survey of college students was conducted during final exam week to assess the

Question

A survey of college students was conducted during final exam week to assess the number of cups of coffee consumed each day. The mean number of cups was 5 with a standard deviation of 1.5 cups. The distribution was normal.

a. What proportion of students drank 7 or more cups of coffee per day?

b. What proportion of students drank 2 or more cups of coffee per day?

c. What proportion of students drank between 2 and 7 cups of coffee per day?

d. How many cups of coffee would an individual at the 60th percentile rank drink?

e. What is the percentile rank for an individual who drinks 4 cups of coffee a day?

f. What is the percentile rank for an individual who drinks 7.5 cups of coffee a day?

Explanation / Answer

A survey of college students was conducted during final exam week to assess the number of cups of coffee consumed each day. The mean number of cups was 5 with a standard deviation of 1.5 cups. The distribution was normal.

a. What proportion of students drank 7 or more cups of coffee per day?

Z value for 7, z=(7-5)/1.5 =1.33

P(x>7) = P( z >1.33) = 0.0918

b. What proportion of students drank 2 or more cups of coffee per day?

Z value for 2, z=(2-5)/1.5 = -2

P(x>2) = P( z > -2) = 0.9772

c. What proportion of students drank between 2 and 7 cups of coffee per day?

P( 2 <x<7)

= P( x <7) – P( x < 2)

=P( z <1.33) – P( z < -2)

= 0.9082 - 0.0228

= 0.8854

d. How many cups of coffee would an individual at the 60th percentile rank drink?

Z value for 60th percentile =0.253

X =5+0.253*1.5 = 5.3795

e. What is the percentile rank for an individual who drinks 4 cups of coffee a day?

Z value for 4, z=(4-5)/1.5 =-0.67

percentile rank for z=-0.67 is 25.14%

f. What is the percentile rank for an individual who drinks 7.5 cups of coffee a day?

Z value for 7.5, z=(7.5-5)/1.5 =1.67

percentile rank for z=1.67 is 95.25%

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