The ACT has a mean score 20 and a standard deviation of 5. What score you have t
ID: 3226865 • Letter: T
Question
The ACT has a mean score 20 and a standard deviation of 5. What score you have to make in order to score in the 90th percentile. Seventy five percent of the people in the US who made a New Year's last year kept it. You randomly select 70 people in the US who made a resolution last year and ask each if he/she kept the resolution (Use normal on t binomial distribution) Find the probability that at most 50 will say yes at least 50 will say yes exactly 50 will say yes less than 50 will say yes. The Sociology Department has a strict makeup exam policy. From a random sample ofExplanation / Answer
18).
Z value for 90th percentile= 1.282 ( from standard normal table)
x =mean+z*sd = 20+1.282*5 =26.41
19).
p=0.75, n=70
Expectation = np = 52.5
Variance = np(1 - p) = 13.125
Standard deviation = 3.6228
With continuity correction, z value for 50.5, z =(50.5-52.5)/3.6228 = -0.55
P( x 50)=P( z < -0.55) =0.2912
20).
With continuity correction, z value for 49.5, z =(49.5-52.5)/3.6228 = -0.83
P( x 50)=P( z >-0.83) =0.7967
21).
P( x=50) =P( 49.5<x<50.5) = P( -0.83<z<-0.55)
=P( z <-0.55) –P( z< 0.83) = 0.2912 - 0.2033
= 0.2912 - 0.2033
=0.0879
22).
With continuity correction, z value for 49.5, z =(49.5-52.5)/3.6228 = -0.83
P( x <50)=P( z <-0.83) = 0.2033
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