A large population of variable x is characterized by its known mean value of 6.1 units and a standard deviation of 1.0 units and a normal distribution. Determine the range of values containing 70% of the population of x

-6.134 to +6.134

Step-by-step explanation:

given that a large population of variable x is characterized by its known mean value of 6.1 units and a standard deviation of 1.0 units and a normal distribution

X is Normal with mean  =6.1 and std dev = 1 unit

We are to determine the range of values containing 70% of the population of x

We know that normal distribution curve is bell shaped symmetrical about the mean.

So to find 70% range we can use 35% on either side of the mean

Using std normal distribution table the value of z for which probability from 0 to z is 0.35 is 1.034

Hence corresponding x value is

i.e. 70% values lie between

-6.134 to +6.134