Question

The following is a stats problem:

Answer the question for a normal random variable x with a mean mu and a standard deviation sigma specified below. (Round your answer to four decimal places.)

mu=1.3 and sigma=0.16

Find P(x>1.31).

Answer 1

The probability P(Z>0.0625), and this is equivalent to P(x>1.31).

To find P(x > 1.31) for a normal random variable x with mean μ = 1.3 and standard deviation = 0.16, you can use the standard normal distribution Z-table or a calculator. and the

The standard normal distribution is defined as Z =x-μ/σ, where X is the random 3 σ variable, u is the mean, and a is the standard deviation.

In this case, you want to find P(x > 1.31), so you need to convert 1.31 to the standard normal distribution using the formula:

Z = 1.31-1.3 0.16

Calculate Z and then find the probability P(Z > Z1.31) using a Z-table or a calculator.

Z= 1.31-1.3/ 0.16

Z= 0.01 /0.16 = 0.0625

Now, look up the probability P(Z > 0.0625) in the Z-table or use a calculator to find the area to the right of Z = 0.0625.

Round your answer to four decimal places.

Please note that the Z-table or calculator should give you the probability

P(Z>0.0625), and this is equivalent to P(x>1.31).