Question
In: Statistics and Probability
The mean undergraduate cost for tuition, fees, room, and board for four-year institutions was $26,489 for...
The mean undergraduate cost for tuition, fees, room, and board for four-year institutions was $26,489 for a recent academic year. Suppose that that LaTeX: \sigmaσ =$3204 and that 36 four-year institutions are randomly selected. Find the probability that the sample mean cost for these 36 schools is
a) Less than $25,000 P(x(bar) < 25000)= , Calcuator part
Answer= , round your answer to 4 decimal places
b) Greater than $26,000 P(x(bar) > 26000)= , Calcuator part
Answer= , round your answer to 4 decimal places
c) Between $23,000 and $27,600
P( 23000<x(bar)< 27600)= , Calcuator part
Answer= , round your answer to 4 decimal places
Solutions
Expert Solution
This is a normal distribution question with
Sample size (n) = 36
Since we know that
a)
P(x < 25000.0)=?
The z-score at x = 25000.0 is,
z = -2.7884
This implies that
b)
P(x > 26000.0)=?
The z-score at x = 26000.0 is,
z = -0.9157
This implies that
P(x > 26000.0) = P(z > -0.9157) = 1 - 0.1799121325150559
c)
P(23000.0 < x < 27600.0)=?
This implies that
P(23000.0 < x < 27600.0) = P(-6.5337 < z < 2.0805) = P(Z < 2.0805) - P(Z < -6.5337)
P(23000.0 < x < 27600.0) = 0.9812601521824957 - 3.208220514753297e-11
PS: you have to refer z score table to find the final probabilities.
Please hit thumps up if the answer helped you
orchestra answered 1 year agoRelated Solutions
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