In: Statistics and Probability
The SAT scores for students are normally distributed with a mean of 1000 and a standard deviation of 200. What is the probability that a sample of 36 students will have an average score between 970 and 1010? Round your answer to 3 decimal places.
Solution :
Given that,
mean = = 1000
standard deviation = = 200
n = 36
= = 1000
= / n = 200 / 36 = 33.33
P(970 < < 1010)
= P[(970 - 1000) / 33.33 < ( - ) / < (1010 - 1000) / 33.33 )]
= P(- 0.90 < Z < 0.30)
= P(Z < 0.30) - P(Z < - 0.90)
Using z table,
= 0.618 - 0.184
= 0.434