need help solving for this problem. please help. not sure on the steps. normally
ID: 3130712 • Letter: N
Question
need help solving for this problem. please help. not sure on the steps.
normally dis 24. A well known 24. A well-known test of intelligence is constructed to have normally ributed scores with a mean of 100 and a standard deviation of 16 a. What is the probability that someone picked at random will have an b. There are 1Os so high that the probability is 05 that they will occur e. What is the probability that someone picked at random will have an d. What is the probability of selecting two people at random IO of 122 or higher? in a random sample of people. Such 1Qs are beyond what value? IQ between 90 and 1102 i. with both having I0s of 122 or greater? ii. with both having IOs between 90 and 110? ili. with one having an 1O of 122 or greater and the other having an O between 90 and 110? e. An elementary school creates a special curriculum for talented and gifted students. Part of the entry requirement for the curriculum is to be in the 90th percentile for IO. What IQ score will a child require to be considered for this curriculum?Explanation / Answer
A)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 122
u = mean = 100
s = standard deviation = 16
Thus,
z = (x - u) / s = 1.375
Thus, using a table/technology, the right tailed area of this is
P(z > 1.375 ) = 0.084565722 [ANSWER]
******************
b)
First, we get the z score from the given left tailed area. As
Left tailed area = 1 - 0.05 = 0.95
Then, using table or technology,
z = 1.644853627
As x = u + z * s,
where
u = mean = 100
z = the critical z score = 1.644853627
s = standard deviation = 16
Then
x = critical value = 126.317658 [ANSWER]
*******************
c)
We first get the z score for the two values. As z = (x - u) / s, then as
x1 = lower bound = 90
x2 = upper bound = 110
u = mean = 100
s = standard deviation = 16
Thus, the two z scores are
z1 = lower z score = (x1 - u)/s = -0.625
z2 = upper z score = (x2 - u) / s = 0.625
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.265985529
P(z < z2) = 0.734014471
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.468028942 [ANSWER]
*******************
d)
i.
From a), the probability of finding one such person is 0.084565722. Hence, for 2 people,
P = 0.084565722^2 = 0.007151361 [ANSWER]
*******************************************
Hi! Please submit the next part as a separate question. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.