Question

A survey conducted of 1,000 college students asked those who regularly drink alcohol, how many alcoholic beverages they consume each week. From this survey, on average (mean), these students consume five beverages each week. These data are normally distributed. The mean, median and mode are equal, and the standard deviation is 1.

1. How many of these students consume five or more alcoholic beverages each week?

2. What is the probability that a student in this study will consume five or more alcoholic beverages each week? (decimal)

3. How many of these adolescents consume five or less alcoholic beverages each week?

4. What is the probability that a student in this study will consume five or less alcoholic beverages each week? (decimal)

5. How many of these adolescents consume between four and six alcoholic beverages each week? 6. What is the probability that a student in this study will consume from four to six alcoholic beverages each week? (decimal)

Answer 1

Let X be the number of alcoholic beverages students consume each week.

X~ N (5 , 1²)

Sample size = 1000

1. Number of students consume five or more alcoholic beverages each week = P(X 5) *1000

where

  

  

So, number of students consume five or more alcoholic beverages each week = 0.5*1000 = 500

2. The probability that a student in this study will consume five or more alcoholic beverages each week , P(X 5)

  

  

3. Number of students consume five or less alcoholic beverages each week = P(X 5) *1000

where

  

  

So, number of students consume five or less alcoholic beverages each week = 0.5*1000 = 500

4. The probability that a student in this study will consume five or less alcoholic beverages each week , P(X 5)

  

  

5. Number of students consume between four and six alcoholic beverages each week = P(4<X<6) *1000

where

  

  

So, number of students consume between four and six alcoholic beverages each week = 0.6826*1000 = 682.6 683

6. The probability that a student in this study will consume from four to six alcoholic beverages each week, P(4<X<6)