Answer:
$142 ; 0.749 ; Normal ; 0.090938
Step-by-step explanation:
Mean and standard deviation :
The mean of the distribution x = $142, because the sample size is sufficiently large, the distribution will be approximately normal (central limit theorem).
Standard deviation of distribution : σ/ sqrt(n)
= 29 / sqrt(1500)
= 0.749
B.)
Shape of sampling distribution of X.
The shape of the sampling distribution will be approximately normal due to the large sample size used. This is according to the central limit theorem whereby distribution of sample converges to normal with increasing sample size. Mean ~ N(142, 0.749²)
C.)
P(X > 143)
Using the relation :
Z = (x - mean) / standard error
Z = 143 - 142) / 0.7489
Z = 1.335
P(Z > 1.335) :
Using the Z probability calculator :
P(Z > 1.335) = 0.090938
