In: Math
# Example of normal distribution are as follows
Example 1
An average life of light bulb manufactured by company will 300 days with standard deviation of 50 day . Assuming that bulb life is normally distributed what is the probability that an life of light bulb will at most 365 days?
Ans: Given a mean score of 300 days and a standard deviation of 50 days, we want to find the cumulative probability that bulb life is less than or equal to 365 days. Thus, we know the following:
We enter these values into the Normal Distribution Calculator and compute the cumulative probability. The answer is: P( X < 365) = 0.90. Hence, there is a 90% chance that a light bulb will burn out within 365 days.
Example 2
Suppose scores on an IQ test are normally distributed. If the test has a mean of 100 and a standard deviation of 10, what is the probability that a person who takes the test will score between 90 and 110?
Solution: Here, we want to know the probability that the test score falls between 90 and 110. The "trick" to solving this problem is to realize the following:
P( 90 < X < 110 ) = P( X < 110 ) - P( X < 90 )
We use the Normal Distribution Calculator to compute both probabilities on the right side of the above equation.
We use these findings to compute our final answer as follows:
P( 90 < X < 110 ) = P( X < 110 ) - P( X <
90 )
P( 90 < X < 110 ) = 0.84 - 0.16
P( 90 < X < 110 ) = 0.68
Thus, about 68% of the test scores will fall between 90 and 110.