Question

20) 20) Suppose the distribution of of serum cholesterol values in undergraduate men is approximately normally distributed with mean 190 mg/dL and standard deviation 0 - 40 mg/dL. You take a simple random sample of n 49 individuals from this population. What is the probability of getting a sample mean that is less than 200 mg/dL. Hind: Use table on page 158 of your textbook A) 0.9599 B) 0.0401 C) 0.7986 D) 0.5678

Answer 1

Answer:

given that:

Suppose the distribution of serum cholesterol values in undergraduate men is approximately Normally distributed with mean μ = 190 mg/dL and standard deviaiton σ = 40 mg/dL. You take a simple random sample random sample of n=49 individuals from this population.

$P(\bar{X}< 200)$

Normal Distribution, $\mu =190 ,\sigma = 40, n= 49$

we convert this to standard normal using
z = i - Hi/o 0/-
$= \bar{x}-\mu /\sigma /\sqrt{n}$

$z=\frac{200-(190)}{40/\sqrt{49}} =1.75$

Area to the left of 1.75

0.5 0.4 0.3 y 0.2 - 0.1 0.0 1.75 -0.1 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

$P(\bar{X}< 200)=P(Z< 1.75)=0.9599$ ( from z - table)

option 'A' is correct