Statistics and Probability Answers

A company produces one-kilogram sugar packets. The specifications on the net content are 1000 ≠ 5 grams. Assuming that the net content follows normal distribution with mean weight as 1005 grams and the process capability equal to 30 grams, find out the proportion of packets that have weight less than lower specification limit. What should be the mean if this proportion is to be reduced to 0.01?

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We have n letters for constructing words, letter a occurs α times, letter b occurs β times, and the remaining letters are distinct. How many different r-letter words containing h times letter a and k times letter b are possible?

In a sample of college seniors, responded positively when asked if they have spring fever. Based upon this, compute a confidence interval for the proportion of all college seniors who have spring fever. Then complete the table below.
Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places.

What is the lower limits 95% confidence interval ?
What is the higher limit 95% confidence interval ?

In a sample of 350 college seniors, 290 responded positively when asked if they have spring fever. Based upon this, compute a confidence interval for the proportion of all college seniors who have spring fever. Then complete the table below.
Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places.

What is the lower limit of 95% confidence interval ?
What is the higher limit of 95% confidence interval ?

A medical doctor wishes to test the claim that the standard deviation of the systolic blood pressure of deep sea divers is less than 450. To do so, she selected a random sample of 20 divers and found s = 432.

Assuming that the systolic blood pressures of deep sea divers are normally distributed, if the doctor wanted to test her research hypothesis at the .01 level of significance, what is the critical value?

The number of total accidents during the first half of 2008 are as given in the Table below.
Data on Fatal Accidents
Month Jan Feb Mar Apr May June
No. of fatal accidents 2 4 3 4 3 2

i) Draw the graph and comment.
ii) Prepare the table of forecasts and errors by applying simple exponential smoothing for the data given in (i) (take the exponential smoothing constant as 0.1).

A random sample of 700 units from a large consignment showed that 200 were damaged. Find 95 % confidence interval for the proportion of damaged unit in the consignment

(ii) Show that P(B) = P(B/A). P(A) + P(B/AC) P(AC) = P(A).
Two floppies are selected at random without replacement from a box containing 7 good and 3 defective floppies. Let A be the event that the first floppy drawn is defective, and let B be the event that the second floppy drawn is defective.

(i) Find the conditional probabilities P(B/A) and P(B/AC)

An economist want to estimate a multiple regression equation in which the (3)
amount saved by the ith family depends on the family’s income, whether the
family is graduate or non graduate, and whether the family is headed by a male
or female. Explain how a regression equation of this sort can be estimated. What
is the dependent variable ? What are the independent variables? What assumption
must be made ?

A company produces one-kilogram sugar packets. The specifications on the net content are 1000 ≠ 5 grams. Assuming that the net content follows normal distribution with mean weight as 1005 grams and the process capability equal to 30 grams, find out the proportion of packets that have weight less than lower specification limit. What should be the mean if this proportion is to be reduced to 0.01?