Question

Given a normal distribution with a mean of 125 and a standard deviation of 14, what percentage of values is within the interval 111 to 139? (4 points)

	32%
	50%
	68%
	95%
	99.7%

Answer 1

A normal population is given with a mean of 125 and a standard deviation of 14.

To find what percentage of values is within the interval 111 to 139.

Let, X be the random variable.

So, X follows normal with a mean of 125, and standard deviation of 14.

So, (X-125)/14~normal(0,1)

To find P(111<X<139)

=P(111-125<X-125<139-125)

=P(-14<X-125<14)

=P(-14/14<(X-125)/14<14/14)

=P(-1<Z<1)

Where, Z is the standard normal variate.

=phi(1)-phi(-1)

Where, phi is the distribution function of the standard normal variate.

=phi(1)-1+phi(1)

=2*phi(1)-1

=2*0.8413-1

=1.6826-1

=0.6826.

So, the probability that the values will lie within the interval 111 to 139 is 0.6826.

So, the percentage of values that lie between 111 and 139 is 0.6826*100=68.26%~68% approximately.

So, the answer is (c) 68%