Given a mean of -7.8 and a standard deviation of 16 from a normally distributed sample,what is the probability of an observation being below 12.0?
A) 0.51
B) 0.61
C) 0.71
D) 0.81

Question

Quizplus · Accepted Answer

First, we need to standardize the value using the formula:

z = (x - μ) / σ

where: 
x = 12 (the observation we want to find the probability for) 
μ = -7.8 (mean) 
σ = 16 (standard deviation)

So,

z = (12 - (-7.8)) / 16 
z = 1.1175

Next, we look up the probability of z being less than 1.1175 in the standard normal distribution table. We can also use a calculator or software to find this probability, which is approximately 0.8708.

However, we are interested in the probability of the observation being below 12, which is the same as the probability of z being less than 1.1175.

So, the answer is D) 0.81, which is the probability of a standard normal distribution having a value less than 1.1175.

Given a Mean of -7