The National Earthquake Information Center (NEIC) locates...

The National Earthquake Information Center (NEIC) locates roughly between 12,000 and 14,000 earthquakes each year. Based on this, assume that the number of earthquakes each year is normally distributed with a mean of 13,000 and a standard deviation of 250. a) What is the probability that between 12700 and 13130 earthquakes are located in a year? b) What is the probability of a year having more than 13170 earthquakes in a year? c) What is the probability that less than 12730 earthquakes are identified?

Transcript

00:01 Hello students, here pdf of normal distribution is given by 1 by 2 root pi sigma and take the square root e power minus x minus mu by sigma whole square.

00:23 So, the standard normal distribution is a normal distribution with a mean that is equal to 0 and the standard deviation which is equal to 1.

00:34 So, the equation for the standard normal distribution will become x minus mu by sigma.

00:44 This is normal distribution with the mean 0 and the variance or the standard deviation both will be equal to 1 only.

00:53 So, here we are given the mean mu is equal to 13000 and we are given the standard deviation is 250.

01:03 So, the first question probability between 12890 and 13150 earthquakes are located in a year.

01:14 So, this is equal to probability of a less than or equal to z less than or equal to b.

01:21 So, which will be equal to f of b minus f of a.

01:29 So, probability of x minus mu by sigma is less than 12890 minus mu which is 13000 divided by sigma which is 250.

01:51 So, this is equal to probability of z less than or equal to z.

02:06 So, from the standard normal distribution table we can find this 0 .33.

02:14 Then probability of x less than 13150 is equal to probability of x minus mu by sigma that is z is less than 13150 minus 13000 divided by sigma which is 250.

02:41 So, this is equal to probability of z being less than 0 .6 which is equal to 0 .7257...

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