Question

A set of data is normally distributed with a mean of 3.5 and a standard deviation of 0.5. What is the probability that a data value chosen at random is more than 3.1?

a) 0.7877
b) 0.3133
c) 0.7881
d) 0.5755

Answer 1

To find the probability that a data value chosen at random is more than 3.1 in a normal distribution with a mean of 3.5 and a standard deviation of 0.5, we can use the standard normal distribution table or a calculator. The probability is approximately 0.7881.

Step-by-step explanation:

To find the probability that a data value chosen at random is more than 3.1 in a normal distribution with a mean of 3.5 and a standard deviation of 0.5, we can use the standard normal distribution table or a calculator.

We need to find the area under the curve to the right of 3.1, which is the same as finding the area to the left of 3.1 and subtracting it from 1. The formula for calculating the standard normal distribution is:

z = (x - μ) / σ

where z is the z-score, x is the value we are interested in, μ is the mean, and σ is the standard deviation.

Plugging in the values, we get:

z = (3.1 - 3.5) / 0.5 = -0.8

Using the standard normal distribution table or a calculator, we find that the area to the left of -0.8 is approximately 0.2119. Therefore, the area to the right of 3.1 is:

1 - 0.2119 = 0.7881