The SAT scores for students are normally distributed with a mean of 1050 and a standard deviation of 205. What is the probability that a sample of 30 students will have an average score between 1030 and 1060? Round your answer to 3 decimal places.
Group of answer choices
0.058
0.309
0.583
0.761
0.691
Solution :
Given that,
mean = = 1050
standard deviation = = 205
_{} = / n = 205 / 30 = 37.4277
= P[(1030 - 1050) / 37.4277< ( - _{}) / _{} < (1060 - 1050) /37.4277 )]
= P(-0.534 < Z < 0.267)
= P(Z < 0.267) - P(Z < -0.534)
= 0.6053 - 0.2967
0.309
Probability = 0.309
Option 2nd is correct.
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