Question

this is a test review assignment. the purpose of this assignment is to help you prepare for the test. on the test, you wont have access to the videos or helps in the problems. you should try to do these problems without using these videos and additional helps. if you dont know what to do, you can watch the video. if the only way you can do the problems is watching the videos then you are not ready to take the test and should continue studying (you can request new problems and keep working on them after you get credit for the problems without impacting your grade). the mean daily production of a herd of cows is assumed to be normally distributed with a mean of 35 liters, and standard deviation of 4.9 liters. a) what is the probability that daily production is between 40.1 and 43.6 liters? do not round until you get your final answer. answer= (round your answer to 4 decimal places.) warning: do not use the z normal tables...they may not be accurate enough since wamap may look for more accuracy than comes from the table.

Explanation:

Step1: Calculate z - scores

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $\mu = 35$ (mean), $\sigma = 4.9$ (standard deviation).
For $x = 40.1$, $z_1=\frac{40.1 - 35}{4.9}=\frac{5.1}{4.9}\approx1.0408$.
For $x = 43.6$, $z_2=\frac{43.6 - 35}{4.9}=\frac{8.6}{4.9}\approx1.7551$.

Step2: Use the properties of the standard normal distribution

We want $P(40.1Since $P(a < Z < b)=P(Z < b)-P(Z < a)$, we use a calculator with a normal - distribution function (e.g., on a TI - 84 Plus: normalcdf).
$P(Z < 1.7551)-P(Z < 1.0408)$.
Using a calculator, $P(Z < 1.7551)\approx0.9604$ and $P(Z < 1.0408)\approx0.8508$.
So $P(1.0408 < Z < 1.7551)=0.9604 - 0.8508=0.1096$.

Answer:

$0.1096$