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Normal Distribution in Real-Life Examples

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Very difficult subject material for me.

1. Given a normal distribution with mean=100 and variance/S.D. = 10, what is the probability that a. X>75? B. X<70? C. X<80 or X>110? D. Between what two X values (symmetrically distributed around the mean) are 80% of the values?

2. A statistical analysis of 1,000 long-distance telephone calls made from the headquarters of the Bricks and Clicks Computer Corporation indicates that the length of these call is normally distributed, with mu=240 seconds and variance = 40 seconds.
a. What is the probability that a call lasted less than 180 seconds?
b. What is the probability that a call lasted between 180 and 300 seconds?
d. 1% of all calls will last less than how many seconds?

3.A study of the time spent shopping in a supermarket for a market basket of 20 specific items showed an approximately uniform distribution between 20 minutes and 40 minutes. What is the probability that the shopping times will be
a. between 25 and 30 minutes?
b. less than 35 minutes?
c. What are the mean and standard deviation of the shopping time?

4. Autos arrive at a toll plaza locasted at the entrance to a bridge at a rate of 50 per minutes during the 5:00 - 6:00 p.m. hour. If an auto has just arrived,
a. what is the probability that the next auto will arrive within 3 seconds (0.05 minute)?
b. what is the probability that the next auto will arrive within 1 second (0.0167 minute)?
c. What are your answers to a and b if the rate of arrival of autos is 60 per minute?
d. What are your answers to a and b if the rate of arrival of autos is 30 per minute?

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