Question

Suppose that the TSH (Thyroid Stimulating Hormone) levels among healthy individuals are normally distributed with a mean of 3.1 units/mL. Suppose also that exactly 95% of healthy individuals have TSH levels below 5.8 units/mL. Find the standard deviation of the distribution of TSH levels of healthy individuals. Carry your intermediate computations to at least four decimal places. Round your answer to at least two decimal places.

Answer 1

std deviation = 1.641

Explanation:

Given that the TSH (Thyroid Stimulating Hormone) levels among healthy individuals are normally distributed with a mean of 3.1 units/mL.

If X represents the TSH then X is N(3.1, sigma)

We do not know sigma value, but we are given that exactly 95% of healthy individuals have TSH levels below 5.8 units/mL.

We know as per standard normal distribution score that 95th percentile referes to Z score of 1.645

Using this we can find standard dev

`5.8 = 3.1+1.645*standard dev\\Standard dev = (5.8-3.1)/(1.645) \\=1.641`