An srs of 350 350 high school seniors gained an average of ¯ x = 22.61 x¯=22.61 points in their second attempt at the sat mathematics exam. assume that the change in score has a normal distribution with standard deviation σ = 53.63 . σ=53.63. we want to estimate the mean change in score μ μ in the population of all high school seniors. (a) using the 68 68 – 95 95 – 99.7 99.7 rule or the z - z- table (table a), give a 95 % 95% confidence interval ( a , b ) (a, b) for μ μ based on this sample.

 (16.9914, 28.2286).

Step-by-step explanation:

The formula to find the confidence interval for population mean is given by :-

, where = Sample mean

= Population standard deviation

n= Sample size.

z* = Critical value.

Let μ be the mean change in score  in the population of all high school seniors.

As per given ,  we have

n= 350

The critical z-value for 95% confidence interval is z*= 1.96 [From z-table]

Substitute all the value in formula , we get

Hence, the 95% confidence interval for is (16.9914, 28.2286).

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