(4) A colleges data about the incoming freshman indicates that their high school
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(4) A colleges data about the incoming freshman indicates that their high school GPAs followr wich a mean of 3.2, and a standard deviation of 0.3. The students is the probability that the mean GPA of the group (of the 20 students) is more a normal distribution a 3.2 aighed to freshman writing seminars in groups of 20. (a)What than 3? -0.bo1 0,44 16 3 3.2 229 8 24 (b) If you select one student randomly from the group, what is the probablity that his/her GPA is more than 3? (c) Are your answers to (a) and (b) the same or different? Briefy explain why using the sampling distribution of X.Explanation / Answer
the PDF of normal distribution is = 1/? * ?2? * e ^ -(x-u)^2/ 2?^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)
a.
with group of 20,
mean of the sampling distribution ( x ) = 3.2
standard Deviation ( sd )= 0.3/ Sqrt ( 20 ) =0.0671
sample size (n) = 20
P(X > 3) = (3-3.2)/0.3/ Sqrt ( 20 )
= -0.2/0.067= -2.9814
= P ( Z >-2.9814) From Standard Normal Table
= 0.9986
b.
mean of the sampling distribution ( x ) = 3.2
standard Deviation ( sd )= 0.3/ Sqrt ( 1 ) =0.3
sample size (n) = 1
GREATER THAN
P(X > 3) = (3-3.2)/0.3/ Sqrt ( 1 )
= -0.2/0.3= -0.6667
= P ( Z >-0.6667) From Standard Normal Table
= 0.7475
c.
both are diffrent, since the sample size is diffrent in each case.
we have the diffrent standard deviation value with the sample size one, with the sample size 20, this result in diffrent probability chances
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