prettylittlepixels
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- Nov 15, 2013
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The scores on a standardized test are normally distributed with a population mean of 720 and a population standard deviation of 60.
Test scores are discrete, so do not forget to make the continuity correction before using the standard normal distribution (which is continuous).
A. What is the probability that an individual, randomly-selected student will score less than 726?
z(726)= (726-720) / 60= 6/60= .1
P(x<726)= P(z<.1)=
z-score that corresponds to .1 is .0398
.5 - .0398 = .4602
B. If we take a sample of 4 randomly-selected students, what is the probability that the sample mean will be less than 726?
z(726)= (726-720) / (60/square root of 4)= 6 / (60/2)= 6/30= 1/5= .2
z-score that corresponds to .2 is .0793
.5-.0793= .4207
C. Why are your answers to Parts A and B above in this problem different?
Please be specific! Do not simply describe the difference in the formulas. Explain WHY the formulas are different.
I have no idea… Because the values of P are almost complements???
D. If we take a sample of 100 randomly-selected students, what is the probability that the sample mean will be less than 726?
z(726)= (726-720) / (60/square root of 100)= 6 / (60/10)= 6/6= 1
z-score that corresponds to 1 is .3413
.5-.3413= .1587
E. Why are your answers to Parts B and D in this problem different?
Please be specific and include the value of the mean and the number 726 in your explanation.
I have no idea… As P increased, the probability of the interval increased?
Test scores are discrete, so do not forget to make the continuity correction before using the standard normal distribution (which is continuous).
A. What is the probability that an individual, randomly-selected student will score less than 726?
z(726)= (726-720) / 60= 6/60= .1
P(x<726)= P(z<.1)=
z-score that corresponds to .1 is .0398
.5 - .0398 = .4602
B. If we take a sample of 4 randomly-selected students, what is the probability that the sample mean will be less than 726?
z(726)= (726-720) / (60/square root of 4)= 6 / (60/2)= 6/30= 1/5= .2
z-score that corresponds to .2 is .0793
.5-.0793= .4207
C. Why are your answers to Parts A and B above in this problem different?
Please be specific! Do not simply describe the difference in the formulas. Explain WHY the formulas are different.
I have no idea… Because the values of P are almost complements???
D. If we take a sample of 100 randomly-selected students, what is the probability that the sample mean will be less than 726?
z(726)= (726-720) / (60/square root of 100)= 6 / (60/10)= 6/6= 1
z-score that corresponds to 1 is .3413
.5-.3413= .1587
E. Why are your answers to Parts B and D in this problem different?
Please be specific and include the value of the mean and the number 726 in your explanation.
I have no idea… As P increased, the probability of the interval increased?