Question

In: Statistics and Probability

The mean weight of a fire ant worker is 3.11 mg with a standard deviation of...

The mean weight of a fire ant worker is 3.11 mg with a standard deviation of .49 mg. Suppose we randomly select 14 different fire ant workers having weights F1, F2, , F14. Let S = F1 + F2 + ...+F14 and let M = S/14. This means S is the sample sum and M is the sample mean of the selected ant weights. (Note: random selection means F1 F14 are independent.). Assume the Fis are normally distributed.

a) What is the expected value of S?

b) What is the standard deviation of S?

c) What is the expected value of M?

d) What is the standard deviation of M?

e) What is the expected value of S-14*3.11?

f) What is the standard deviation of ZZ =

(S - 14*3.11)/(sqrt14*.49)

Solutions

Expert Solution

Solution:-

Given that

The mean weight of a fire ant worker is 3.11 mg with a standard deviation of .49 mg. Suppose we randomly select 14 different fire ant workers having weights F1, F2, , F14. Let S = F1 + F2 + ...+F14 and let M = S/14. This means S is the sample sum and M is the sample mean of the selected ant weights.

a) What is the expected value of S?

E(S) = 14 * 3.11

= 43.54

b) What is the standard deviation of S?

=

= 1.8334

c) What is the expected value of M?

d) What is the standard deviation of M?

SD(M) =

= 0.1310

e) What is the expected value of S-14*3.11 ?

The expected value = 0

f) What is the standard deviation of ZZ = (S-14*3.11)/(sqrt14*.49)?

The standard deviation is 1.

Thanks for supporting...

Please give positive rating...

orchestra answered 1 year ago
Next > < Previous

Related Solutions

The mean weight of a fire ant worker is 3.11 mg with a standard deviation of...
The mean weight of a fire ant worker is 3.11 mg with a standard deviation of 0.49 mg. Let us assume that the weight of any fire ant is independent from the weight of any other fire ant. A typical fire ant colony contains 240,000 fire ant workers. Suppose we look at the weight of each ant in a typical fire ant colony. Let M be the random variable representing the mean weight of all the worker ants in the...
In a sample of 51 babies, the mean weight is 21 pounds and the standard deviation...
In a sample of 51 babies, the mean weight is 21 pounds and the standard deviation is 4 pounds. Calculate a 95% confidence interval for the true mean weight of babies. Suppose we are interested in testing if the true mean weight of babies is 19.4 vs the alternative that it is not 19.4 with an alpha level of .05. Would this test be significant? Explain your answer. Perform the t test and use a t-table to get the p-value
the mean weight of loads of rock is 47.0 tons with a standard deviation of 8.0...
the mean weight of loads of rock is 47.0 tons with a standard deviation of 8.0 tons. if 24 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 46.5 tons. assume that the variable is normally distributed.
Horses in a stable have a mean weight of 950 pounds with a standard deviation of...
Horses in a stable have a mean weight of 950 pounds with a standard deviation of 77 pounds. Weights of horses follow the normal distribution. One horse is selected at random. a. What is the probability that the horse weighs less than 900 pounds? b. What is the probability that the horse weighs more than 1,100 pounds? c. What is the probability that the horse weighs between 900 and 1,100 pounds? d. What weight is the 90th percentile? (round to...
For adult men, total cholesterol has a mean of 188 mg/dL and a standard deviation of...
For adult men, total cholesterol has a mean of 188 mg/dL and a standard deviation of 43 mg/dL. For adult women, total cholesterol has a mean of 193 mg/dL and a standard deviation of 42 mg/dL. The CDC defines “high cholesterol” as having total cholesterol of 240 mg/dL or higher, “borderline high” as having a total cholesterol of more than 200 but less than 240, and “healthy” as having total cholesterol of 200 or less. A study published in 2017...
A particular brand of cigarettes has a mean nicotine content of 15.2 mg with standard deviation...
A particular brand of cigarettes has a mean nicotine content of 15.2 mg with standard deviation of 1.6mg c)What is a mean nicotine content for lowest 3% of all cigarettes? d) What is the probability randomly chosen cigarette has a nicotine content greater than 15.2mg? e) What is the probability that a random sample of 40 of these cigarettes has a mean nicotine content between 15.5 and 15.9 mg?
The chickens at Colonel​ Thompson's Ranch have a mean weight of 1850g, with a standard deviation...
The chickens at Colonel​ Thompson's Ranch have a mean weight of 1850g, with a standard deviation of 150g. The weights of the chickens are closely approximated by a normal curve. Find the percent of all chickens having weights more than 2066g or less than 1420g g.
The mean weight of students from a certain university is 70 kg with a standard deviation...
The mean weight of students from a certain university is 70 kg with a standard deviation of 17 kg. i. ii. iii. Assume that the weights of students in the university are normally distributed. What is the probability that the weight of a randomly chosen student is greater than 100 kg? What is the probability that the weight of a randomly chosen student is between 60 kg and 80 kg? If you were to take a sample of 16 students,...
The mean weight of a 2-year old is 27.5 pounds with a standard deviation of 2.3...
The mean weight of a 2-year old is 27.5 pounds with a standard deviation of 2.3 pounds, although some 2-year olds weigh as much as 39 pounds. A health official randomly selects the medical records of 50 2-year olds to study. What is the probability the mean weight of the health official’s sample is more than 28.5 pounds?    A) 0.001 B) 0.332 C) 0.668 D) 0.999 E) This cannot be determined because the distribution is skewed right due to...
Columbia manufactures bowling balls with a mean weight of 14.6 pounds and a standard deviation of...
Columbia manufactures bowling balls with a mean weight of 14.6 pounds and a standard deviation of 3 pounds. A bowling ball is too heavy to use and is discarded if it weighs over 16 pounds. Assume that the weights of bowling balls manufactured by Columbia are normally distributed (Round probabilities to four decimals) a) What is the probability that a randomly selected bowling ball is discarded due to being too heavy to use? b) The lightest 7% of the bowling...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT