Question 1022507: A certain test is designed to measure the satisfaction of an individual with his/her relationship. Suppose that the scores on this test are approximately normally distributed with a mean 60 of and a standard deviation of 10. An individual with a score of 50 or less is considered dissatisfied with his/her relationship. According to this criterion, what proportion of people in relationships are dissatisfied?
Answer by mathmate(429)   (Show Source):
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Question:
A certain test is designed to measure the satisfaction of an individual with his/her relationship. Suppose that the scores on this test are approximately normally distributed with a mean 60 of and a standard deviation of 10. An individual with a score of 50 or less is considered dissatisfied with his/her relationship. According to this criterion, what proportion of people in relationships are dissatisfied?
Solution:
First we need to find the Z-score of individuals with scores less than 50, calculated as follows:
Z=(X-μ)/σ
where μ=mean
σ=standard deviation.
Hence, for X=50,
Z=(50-60)/10=-1
Next we look up the normal distribution table, which you can find online or on your calculator. Note that we are interested in the lower tail, i.e. all persons with scores 50 or less. You will find that P(Z<-1)=0.1587, which means that, for a large population, 15.87% of the members are dissatisfied with his/her relationship, according to the above mentioned definition of "dissatisfaction".
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