We have 4321 random Americans Mysterio intelligence scores W

We have 4,321 random Americans’ Mysterio intelligence scores. We got these 4,321 Americans from random sampling from the entire U.S.A., so knowing the results from one person doesn’t tell us anything about another person.

We don’t know what type of probability distribution the Mysterio intelligence scores have, but we do know that if we measured them for the entire U.S.A., these would have a mean of 76 and a standard deviation of 5.

We are curious about the mean Mysterio intelligence score for the 4,321-person sample.

We can ______ calculate the probability that this mean score is less than or equal to 76.05. This probability value is ______.

What words and/or numbers best fill in the two blanks above?

1st blank: approximately
2nd blank: 50%

1st blank: approximately
2nd blank: 74%

1st blank: approximately
2nd blank: 100%

1st blank: not
2nd blank: unknown

Solution

We have 4,321 random Americans’ Mysterio intelligence scores. We got these 4,321 Americans from random sampling from the entire U.S.A., so knowing the results from one person doesn’t tell us anything about another person.

We don’t know what type of probability distribution the Mysterio intelligence scores have, but we do know that if we measured them for the entire U.S.A., these would have a mean of 76 and a standard deviation of 5.

We are curious about the mean Mysterio intelligence score for the 4,321-person sample.

We can ______ calculate the probability that this mean score is less than or equal to 76.05. This probability value is ______.

What words and/or numbers best fill in the two blanks above?

              A.            1st blank: approximately   2nd blank: 50%

              B.            1st blank: approximately   2nd blank: 74%

              C.            1st blank: approximately   2nd blank: 100%

              D.            1st blank: not     2nd blank: unknown

Sample size is large ,Z distribution is used.

Z value for 76.05, z=(76.05-76)/5= 0.01

P( x < 76.05) = P( z <0.01) =0.504

There fore the correct answer is

A.            1st blank: approximately   2nd blank: 50%