Suppose that a random sample of size 49 is to be selected from a population with mean 49 and standard deviation 6. what is the approximate probability that xwll be more than 0.5 away from the population mean?

a 0.4403
b) 0.6403
c) 0.8807
d) 0.0664
e) 0.5597
f) none of the above

Option e -  0.5597

Step-by-step explanation:

Given : Suppose that a random sample of size 49 is to be selected from a population with mean 49 and standard deviation 6.

To find :  What is the approximate probability that will be more than 0.5 away from the population mean?

Solution :  

Applying z-score formula,

Here,

As, probability that will be more than 0.5 away from the population mean

i.e. x=49.5,

In z-score table the value of z at 0.58 is 0.7190.

x=48.5,

In z-score table the value of z at -0.58 is 0.2810.

Now, probability that will be more than 0.5 away from the population mean is given by,

Therefore, option e is correct.

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