Respuesta :
Answer:
The probability that the sample mean is less than 50 points = 0.002
Step-by-step explanation:
Step(i):-
Given mean of the normal distribution = 56 points
Given standard deviation of the normal distribution = 12 points
Random sample size 'n' = 36 games
Step(ii):-
Let x⁻ be the random variable of normal distribution
Let x⁻ = 50
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{50-56 }{\frac{12}{\sqrt{36} } }= -3[/tex]
The probability that the sample mean is less than 50 points
P( x⁻≤ 50) = P( Z≤-3)
= 0.5 - P(-3 <z<0)
= 0.5 -P(0<z<3)
= 0.5 - 0.498
= 0.002
Final answer:-
The probability that the sample mean is less than 50 points = 0.002
Answer:
56
2
.001
Step-by-step explanation:
The Central Limit Theorem for Means states that the mean of any sampling distribution of the means is equal to the mean of the population distribution. The standard deviation is equal to the standard deviation of the population divided by the square root of the sample size. So, the mean of this sampling distribution of the means with sample size 36 is 56 points and the standard deviation is 1236√=2 points. The z-score for 50 using the formula z=x¯¯¯−μσ is −3.
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
-3.0 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001
-2.9 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001
-2.8 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002
-2.7 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
-2.6 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004
-2.5 0.006 0.006 0.006 0.006 0.006 0.005 0.005 0.005 0.005 0.005
Using the Standard Normal Table, the area to the left of −3 is approximately 0.001. Therefore, the probability that the sample mean will be less than 50 points is approximately 0.001.
