Stat 225
1 of 11 ID: MST.CPD.UD.03.0010
William is a quality inspector for an appliance manufacturer and is currently testing an oven. The oven starts off at room temperature, which is 70 degrees Celsius. William turns the oven to 167 degrees. The temperature in the oven increases from 70 degrees to 167 degrees over the following 10 minutes at a constant rate, so that the temperature follows a uniform distribution over the interval between 70 degrees and 167 degrees. At a randomly chosen time during that 10 minutes, William records the temperature of the oven.
a)Calculate the probability that the temperature is less than 126 degrees. Give your answer as a decimal to 2 decimal places.
Probability =
b)Calculate the probability that the temperature is somewhere between 93 degrees and 108 degrees. Give your answer as a decimal to 2 decimal places.
Probability =
c)Calculate the probability that the temperature is 117 degrees. Give your answer as a decimal to 2 decimal places.
Probability =
[3 points]- 2 of 11 ID: MST.CPD.UD.01.0010
Select which of the following situations could be modeled using a continuous uniform distribution: | Yes | No | a) | A factory worker tests the lifetime of a set of standard batteries. She finds that the batteries will tend to last around 10 hours, although they may last anywhere between 5 and 15 hours. Around 10 hours is most likely, and the probability that a battery will last around 5 hours or around 15 hours is quite small. | | | b) | An office worker turns up to work between 8:00 am (because this is when the building opens) and 9:00 am (because he has to be in by then). The time that he arrives is determined by several factors, and the likelihood of the time of his arrival is constant over all equal time periods between 8:00 am and 9:00 am. | | | c) | A standard 6-sided die is thrown, and the number of dots on the face that turns up is recorded. Each face has an equal chance of turning up. | | |
[4 points]- 3
William is a quality inspector for an appliance manufacturer and is currently testing an oven. The oven starts off at room temperature, which is 70 degrees Celsius. William turns the oven to 167 degrees. The temperature in the oven increases from 70 degrees to 167 degrees over the following 10 minutes at a constant rate, so that the temperature follows a uniform distribution over the interval between 70 degrees and 167 degrees. At a randomly chosen time during that 10 minutes, William records the temperature of the oven.
a)Calculate the probability that the temperature is less than 126 degrees. Give your answer as a decimal to 2 decimal places.
Probability =
b)Calculate the probability that the temperature is somewhere between 93 degrees and 108 degrees. Give your answer as a decimal to 2 decimal places.
Probability =
c)Calculate the probability that the temperature is 117 degrees. Give your answer as a decimal to 2 decimal places.
Probability =
[3 points]- 2 of 11 ID: MST.CPD.UD.01.0010
Select which of the following situations could be modeled using a continuous uniform distribution: | Yes | No | a) | A factory worker tests the lifetime of a set of standard batteries. She finds that the batteries will tend to last around 10 hours, although they may last anywhere between 5 and 15 hours. Around 10 hours is most likely, and the probability that a battery will last around 5 hours or around 15 hours is quite small. | | | b) | An office worker turns up to work between 8:00 am (because this is when the building opens) and 9:00 am (because he has to be in by then). The time that he arrives is determined by several factors, and the likelihood of the time of his arrival is constant over all equal time periods between 8:00 am and 9:00 am. | | | c) | A standard 6-sided die is thrown, and the number of dots on the face that turns up is recorded. Each face has an equal chance of turning up. | | |
[4 points]- 3