Question

Question 2.1

0 / 1 point

The mean of an exponential distribution is 1.2. What is the standard deviation?

Question 2.2

0 / 1 point

The life of a battery can be modeled by a normal distribution. The mean lifetime is 50 hours with a standard deviation of 6 hours. The manufacturer advertises that they will replace all batteries that last less than 38 hours. If 50,000 batteries were produced, how many would they expect to replace? Choose the best answer.

Question 2.3

0 / 1 point

A bottle of fruit punch contains at least 471 ml. The machine that fills the bottles is set so that the mean volume is 477 ml. The volumes in the bottles are normally distributed with standard deviation 2 ml. What percent of the bottles are underfilled? Choose the best answer.

Question 2.4

0 / 1 point

The current (in mA) measured in a piece of copper wire is known to follow a uniform distribution over the interval [0, 25]. What is the standard deviation of the current? Keep two decimal places.

Answer 1

Question 2.1

In exponential distribution that the mean is equal to the standard deviation.

Standard deviation = 1.2

--------

Question 2.2

µ = 50, σ = 6

P(X < 38) =

= P( (X-µ)/σ < (38-50)/6 )

= P(z < -2)

Using excel function:

= NORM.S.DIST(-2, 1)

= 0.0228

Number of batteries expected to be replaced = 50000*0.0228 = 1140

-------

Question 2.3

µ = 477, σ = 2

P(X < 471) =

= P( (X-µ)/σ < (471-477)/2 )

= P(z < -3)

Using excel function:

= NORM.S.DIST(-3, 1)

= 0.0013 = 0.13%

------------

Question 2.4

Standard deviation = (b - a)/√12 = (25 - 0)/√12 = 7.22