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# Chapter 6, Problem 9 Answers

**Suppose that the mean score for the mathematics test cited in Problem 7 is 610. What is the probability that a random sample of 225 students will have a mean score of more than 625? Less than 600?**

**Given data;**

mean = = 610

standard deviation = = 120

n = 225

= 610

●Standard error = / n = 120 225 = 8.00

**What is the probability that a random sample of 225 students will have a mean score of more than 625?**

P ( > 625 )

= 1 - P ( <625 )

= 1 - P ( - / ) < ( 625 - 610 / 8.00)

= 1 - P ( z < 15 / 8.00 )

= 1 - P ( z < 1.87 )

Using z table

= 1 - 0.9693

= 0.0307

**Probability = 0.0307**

**What is the probability that a random sample of 225 students will have a mean score of less than 625?**

P( < 600 )

P ( - / ) < ( 600 - 610/ 8.00)

P ( z < - 10 / 8.00 )

P ( z < -1.25)

= 0.1056

**Probability = 0.1056**