Probability and Statistics Quiz 2 Chapter 4

The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function: Calculate P (X ≤ 4).

• 0.4625

• 0.9375

• 0.375

• 1.4

Let X have a uniform distribution on the interval [A, B]. Obtain an expression for the (100p)th percentile.

• x=A-(A-B)/p

• x=A(B-A)/p

• x=A+(B-A)p

• x=B-A

Mopeds (small motorcycles with an engine capacity below 50 cm3) are very popular in Europe because of their mobility, ease of operation, and low cost. The article 'Procedure to Verify the Maximum Speed of Automatic Transmission Mopeds in Periodic Motor Vehicle Inspections' (J. of Automobile Engr., 2008: 1615-1623) described a rolling bench test for determining maximum vehicle speed. A normal distribution with mean value 46.8 km/h and standard deviation 1.75 km/h is postulated. Consider randomly selecting a single such moped. What is the probability that maximum speed is at most 50 km/h?

• 0.106

• 1.83

• 0.5

• 0.9664

Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with λ=1 (which is identical to a standard gamma distribution with α= 1), compute P(2 ≤ X ≤ 5).

• 0.270

• 0.129

• 0.291

• 0.720

A machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is .500 in. A bearing is acceptable if its diameter is within .004 in. of this target value. Suppose, however, that the setting has changed during the course of production, so that the bearings have normally distributed diameters with mean value .499 in. and standard deviation .002 in. What percentage of the bearings produced will not be acceptable?

• 0.073

• 0.065

• 0.020

• 0.447