Chapter 16 Part 4 CONTINUOUS RANDOM VARIABLES. When two independent continuous random variables are Normally distributed, so is their sum or difference.

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Presentation transcript:

Chapter 16 Part 4 CONTINUOUS RANDOM VARIABLES

When two independent continuous random variables are Normally distributed, so is their sum or difference. Remember the Normal model?

A company that ships stereos has a packing time that is normally distributed with a mean of 9 minutes and a standard deviation of 1.5 minutes. What is the probability that packing two consecutive systems takes over 20 minutes? Step 1: Find E(P1+P2) and SD(P1+P2)

A company that ships stereos has a packing time that is normally distributed with a mean of 9 minutes and a standard deviation of 1.5 minutes. What is the probability that packing two consecutive systems takes over 20 minutes? Step 2: Model with N(18,2.12)

A company that ships stereos has a packing time that is normally distributed with a mean of 9 minutes and a standard deviation of 1.5 minutes. What is the probability that packing two consecutive systems takes over 20 minutes? Step 3: Find the z-score for 20 minutes

A company that ships stereos has a packing time that is normally distributed with a mean of 9 minutes and a standard deviation of 1.5 minutes. What is the probability that packing two consecutive systems takes over 20 minutes? Step 4: Use a z- table to find the probability

A company that ships stereos has a packing time that is normally distributed with a mean of 9 minutes and a standard deviation of 1.5 minutes. What is the probability that packing two consecutive systems takes over 20 minutes? Step 5: State your conclusion There is a 17.36% chance that it will take a total of over 20 minutes to pack two consecutive stereo systems.

A company that ships stereos has a packing time that is normally distributed with a mean of 9 minutes and a standard deviation of 1.5 minutes. The boxing time is also normally distributed with a mean of 6 minutes and a standard deviation of 1 minute. What percentage of the stereo systems take longer to pack than to box? Step 1: Find E(P-B) and SD(P-B)

A company that ships stereos has a packing time that is normally distributed with a mean of 9 minutes and a standard deviation of 1.5 minutes. The boxing time is also normally distributed with a mean of 6 minutes and a standard deviation of 1 minute. What percentage of the stereo systems take longer to pack than to box? Step 2: Model with N(3,1.8)

A company that ships stereos has a packing time that is normally distributed with a mean of 9 minutes and a standard deviation of 1.5 minutes. The boxing time is also normally distributed with a mean of 6 minutes and a standard deviation of 1 minute. What percentage of the stereo systems take longer to pack than to box? Step 3: Calculate the z- score for 0 minutes

A company that ships stereos has a packing time that is normally distributed with a mean of 9 minutes and a standard deviation of 1.5 minutes. The boxing time is also normally distributed with a mean of 6 minutes and a standard deviation of 1 minute. What percentage of the stereo systems take longer to pack than to box? Step 4: Use a z-table to find the probability

A company that ships stereos has a packing time that is normally distributed with a mean of 9 minutes and a standard deviation of 1.5 minutes. The boxing time is also normally distributed with a mean of 6 minutes and a standard deviation of 1 minute. What percentage of the stereo systems take longer to pack than to box? Step 5: State your conclusion There is a 95.25% chance that the stereo systems will require more time for packing than boxing.

Today’s Assignment:  Pg. 386 #42