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A manufacturer claimed that at least 95% of the equipment which he supplied to a factory conformed to specification. State the null and alternative hypothesis for each of the following statements
There are two octahedral dice with faces marked 1 through 8. They are constructed such that the side 8 is 1.5 times as probable as the 2 through 7 and the sum of the probabilities of the 1 and the 8 equals that of the pairs on opposing faces. Let x be the sum of the faces when we roll the two dice.
Find the following:
a. Probability distribution of x
b. Mean of x
c. Variance of x
A new stockbroker (XYZ) claims that his brokerage fees are lower than that of your current stock broker's (ABC). Data available from an independent research firm indicates that the mean and std-dev of all ABC broker clients are $18 and $6, respectively. A sample of 100 clients of ABC is taken and brokerage charges are calculated with the new rates of XYZ broker. If the mean of the sample is $18.75 and std-dev is the same ($6), can any inference be made about the difference in the average brokerage bill between ABC and XYZ broker?
The automatic opening device of a military cargo parachute has been designed to open
when the parachute is 202 m above the ground. Suppose opening altitude actually has a normal
distribution with mean value 202 m and standard deviation 31 m. Equipment damage will occur
if the parachute opens at an altitude of less than 102 m. What is the probability that there is
equipment damage to the payload of at least one of five independently dropped parachutes?
Suppose the force acting on a column that helps to support a building is normally
distributed with mean 16.0 kips and standard deviation 1.35 kips. What is the probability that the
force
a. Is at most 17 kips?
b. Is between 11 and 13 kips?
c. Differs from 16.0 kips by at most 1.6 standard deviations?
Nicole Nelson has come into an inheritance from her grandparents. She is attempting to decide among several investment alternatives. The return after one year is dependent primarily on the interest rate during the next year. The rate is currently 7%, and she anticipates it will stay the same or go up or down by at most 2 points. The various investment alternatives plus their returns ($10,000s) given the interest rate changes are shown in the following table. Interest Rates Investments 5% 6% 7% 8% 9% Money market fund 1.7 2.8 3.0 3.6 4.5 Stock growth fund -5 -3 3.5 5 7.5 Bond fund 5 4 3.5 3 2 Government fund 4 3.6 3.2 2.8 2.1 Risk fund -12 -7 4.2 9.3 16.7 Savings bonds 3 3 3.2 3.4 3.5
A production plant has nine departments and the present layout is shown in the following figure. A D G B E H C F I
The movement of materials between the departments is shown in the load summary table below. To From B F I A 90 D 180 200 E 90 270 H 630 Obtain a good layout considering the unit costs of movement is Rs.10 per unit distance per load for all movements.
One day, Professor brought a box that contains 6 yellow and 7 green marbles in his class in Statistics and Probability subject. He asked one student to draw three marbles, with replacement, in the box. What is the probability when the student drawn 1 yellow and 2 green marbles? Convert your answer in decimals with three (3) significant figures.
A shipment of 25 similar laptop computers to a retail outlet contains 5 that are defective. If a school makes a random purchase of 3 of these computers, find the probability when the school accidentally purchased 1 defective and 2 are nondefective computers? Convert your answer in decimals with three (3) significant figures.
A production plant has nine departments and the present layout is shown in the following figure. A D G B E H C F I
The movement of materials between the departments is shown in the load summary table below. To From B F I A 90 D 180 200 E 90 270 H 630 Obtain a good layout considering the unit costs of movement is Rs.10 per unit distance per load for all movements.
