A simple random sample of size n=14 is obtained from a population with μ=62 and σ=19. ​(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample​ mean? Assuming that this condition is​ true, describe the sampling distribution of x. ​(b) Assuming the normal model can be​ used, determine ​P(x<65.9​). ​(c) Assuming the normal model can be​ used, determine ​P(x≥64.4​). ​(a) What must be true regarding the distribution of the​ population?   A. The sampling distribution must be assumed to be normal.   B. Since the sample size is large enough, the population distribution does not need to be normal.   C. The population must be normally distributed and the sample size must be large.   D. The population must be normally distributed.   Assuming the normal model can be​ used, describe the sampling distribution x. Choose the correct answer below.     A. Normal​, with μx=62 and σx=1419   B. Normal​, with μx=62 and σx=1914   C. Normal​, with μx=62 and σx=19 ​(b) ​ P(x<65.9​)=nothing ​(Round to four decimal places as​ needed.)   ​(c) ​P(x≥64.4​)=nothing ​(Round to four decimal places as​ needed.)     Click to select your answer(s).

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A simple random sample of size
n=14
is obtained from a population with
μ=62
and
σ=19.
​(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample​ mean? Assuming that this condition is​ true, describe the sampling distribution of
x.
​(b) Assuming the normal model can be​ used, determine
​P(x<65.9​).
​(c) Assuming the normal model can be​ used, determine
​P(x≥64.4​).
​(a) What must be true regarding the distribution of the​ population?
 
A.
The sampling distribution must be assumed to be normal.
 
B.
Since the sample size is large enough, the population distribution does not
need to be normal.
 
C.
The population must be normally distributed and the sample size must be large.
 
D.
The population must be normally distributed.
 
Assuming the normal model can be​ used, describe the sampling distribution
x.
Choose the correct answer below.
 
 
A.
Normal​,
with
μx=62
and
σx=1419
 
B.
Normal​,
with
μx=62
and
σx=1914
 
C.
Normal​,
with
μx=62
and
σx=19
​(b)
​ P(x<65.9​)=nothing
​(Round to four decimal places as​ needed.)
 
​(c)
​P(x≥64.4​)=nothing
​(Round to four decimal places as​ needed.)
 
 
Click to select your answer(s).
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