Question

1)

The mean per capita income is 21,053 dollars per annum with a standard deviation of 805 dollars per annum.

What is the probability that the sample mean would be less than 20876 dollars if a sample of 71 persons is randomly selected? Round your answer to four decimal places.

2) Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.

P(X<5), n=8, p=0.4

3)

The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 28,631miles, with a variance of 16,834,610

What is the probability that the sample mean would be less than 28,455 miles in a sample of 178 tires if the manager is correct? Round your answer to four decimal places.

Answer #1

1)

P(x< 20876)

= P(z< ( x -mean)/(sigma/sqrt(n))

= P(z < ( 20876 - 21053)/(805/sqrt(71))

= P(z < -1.85)

= 0.0320

2)

As per binomial distribution,

P(X=r) = nCr * p^r * (1-p)^(n-r)

P(x< 5) = 8C0 * 0.4^0 * (1-0.4)^8 + 8C1 * 0.4^1* (1-0.4)^7 + 8C2 * 0.4^2 * (1-0.4)^6 + 8C3 * 0.4^3 * (1-0.4)^5 + 8C4 * 0.4^4 * (1-0.4)^4

P(x< 5) = 0.8263

3)

P(x<28455)

= P(z< ( x -mean)/(sigma/sqrt(n))

= P(z< ( 28455 - 28631)/(4103.0001/sqrt(178))

= P(z< -0.57

= 0.2836

The mean per capita income is 17,145dollars per annum with a
standard deviation of 505 dollars per annum. What is the
probability that the sample mean would differ from the true mean by
greater than 40 dollars if a sample of 466 persons is randomly
selected? Round your answer to four decimal places.

the mean per capita income is 21053 dollars per annum with a
standard deviation of 805 dollars per annum, what is the
probability that the samele mean would differ from the true mean by
greater than 167 is a sample of 71 persons is selected

the mean per capita income is 21,604 dollars per annum
with a standard deviation of 727 dollars per annum. what is the
probability that the sample mean would differ from the true mean by
less than 36 dollars if a sample of 193 persons is randomly
selected?

The mean per capita consumption of milk per year is 153 liters
with a standard deviation of 2727 liters.
If a sample of 90 people is randomly selected, what is the
probability that the sample mean would be less than
146.97 liters? Round your answer to four decimal
places.

The mean per capita
consumption of milk per year is 141 liters with a standard
deviation of 20 liters.
If a sample of 198
people is randomly selected, what is the probability that the
sample mean would differ from the true mean by greater
than 3.81 liters? Round your answer to four decimal
places.

PLEASE DOUBLE CHECK ANSWER & NO HANDWRITTEN ANSWERS.
THANKS!
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