continuous random variables
numerical variables who values fall within a range or interval; MEASURMENTS
density curves
always on or above the horizontal axis
-has an area exactly equal to one underneath it
-describes overall distribution
-describes what proportions fall within range
unusual density curves
-Can be any shape
-Are generic continuous distributions
-Probabilities are calculated by finding the area under the curve
uniform distribution
A continuous distribution that is evenly (uniformly) distributed
-has a density curve in shape of a rectangle
-calculate area under the curve
in a uniform distribution, the mean is always ________ than the median
equal to
in a continuous distribution, to find the probability of an event occurring one would find the _______________ for respective values
area under the curve
a density curve is drawn on or above the ______________ axis
horizontal
no matter what shape of a density curve, the area underneath it must be equal to ___________
one
in a continuous distribution, the probability that the random variable x equals a value is always ______
zero
in a continuous distribution, the probability statements P(x>5) and P(x greater than or equal to 5) will produce ________________ answers
same
problem: the manufacturing process for golf balls produces golf balls with diameters that are uniformly distributed with a mean of 3.5 cm and a range of .3 cm.
1. draw and label the density curve for information above
2. what is the probability that the g
1. draw graph with rectangle on it, middle number should be 3.5 then half the range and go up and below that number so to the right should be 3.65 and left is 3.35 and the range should be 1/.3
2. P(x>3.45) A= (.2)(1/.3)= .667
3. P(x<3.6) A= (.25)(1/.3)= .
problem(uniform distribution): The manager of a local soft drink bottling company believes that when a new beverage-dispensing machine is set to dispense 7 ounces, it in fact dispenses an amount x at random anywhere between 6.5 and 7.5 ounces inclusive. S
Graph looks like mean of 7 and to the right is 7.5 and to left is 6.5 so range is 1 so y axis is 1/1
1. continuous
2. M= 6.5+7.5/2 = 7 SD= square root of (1)^2/12= .289
3. P(x greater than or equal to 6.75) = A= (.75)(1) = .75
4. P(X> 7.25) A= (.25)(1)= .