Assume the data set described is normally distributed with the given mean and st

Question

Assume the data set described is normally distributed with the given mean and standard deviation, and with n total values. Find the approximate number of data values that will fall in the given range.

Mean = 110

Standard deviation = 7

n = 210

Range: 96 to 124

In this case, we expect about how many data values to fall between 96 and 124.

Assume the data set described is normally distributed with the given mean and standard deviation, and with n total values. Find the approximate number of data values that will fall in the given range.

Mean = 110

Standard deviation = 7

n = 210

Range: 96 to 124

In this case, we expect about how many data values to fall between 96 and 124.

Explanation / Answer

Mean ( u ) =110
Standard Deviation ( sd )=7
Number ( n ) = 210
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 96) = (96-110)/7
= -14/7 = -2
P(X < 124) = (124-110)/7
= 14/7 = 2

Also,
The given range corresponds to those values that lie within 2 standard deviations of the
mean
By empirical rule we know that 95% of values lie within 2 standard deviation
Hence
The number of data value that lie within range: 96 to 124 is (0.95)210 = 199.5~200
Therefore,
200 values lie in the range 96 to 124

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