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Question 1
The height of a typical American male adult is normally distributed with a mean of 68 inches and a standard deviation of 5 inches. We observe the heights of 12 American male adults.
a) What is the probability that exactly half the male adults will be less than 62 inches tall? Blank 1
b) Let Y be the number of the 12 male adults who are less than 62 inches tall. Determine the mean Blank 2 and standard deviation of Y Blank 3.
Question 2
A sporting goods store sells two competing brands of softball bats. Let x1 and x2 be the numbers of the two brands sold on a typical day at the store. Based on the store historical data, the conditional probability distribution of x1 given x2 is assessed and provided in the table below. The marginal distribution of is also given in the bottom row of the table.
Sales of Brand 1, Given sales of Brand 2 x2= 0 x2= 1 x2= 2 x2= 3 x1= 0 0.05 0.15 0.25 0.30 x1= 1 0.10 0.25 0.55 0.57 x1= 2 0.60 0.50 0.15 0.10 x1= 3 0.25 0.10 0.05 0.03 Marginal Distribution of x2 0.20 0.30 0.30 0.20 Are x1 and x2independent random variables Blank 1
x2= 0
x2= 1
x2= 2
x2= 3
x1= 0
0.05
0.15
0.25
0.30
x1= 1
0.10
0.55
0.57
x1= 2
0.60
0.50
x1= 3
0.03
Marginal Distribution of x2
0.20
Find the equation of the tangent plane to the central conicoid x2 - 4y2 + 3z2 + 2 = 0 at the point (1,2,0). Find whether the plane 2x + 3y + 2z =3 touches the central conicoid 2x2 + 3y2 + z2 = 1 or not.
Probability - Frequency Of Dice Rolls, When a pair of dice is rolled, the total will range from 2 (1,1) to 12 (6,6). It is a fact that some numbers will occur more frequently than others as the dice are rolled over and over.
A ranger in tower A spots a fire at a direction of 358 degrees. A ranger in tower B, located 40 mi at a direction of 58 degrees from tower A, spots the fire at a direction of 291 degrees. How far from tower A is the fire? How far from tower B?
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