Question: ### Problem 5 RStudio a) b ) c) Must be able to put code where it says # Insert R code below this line L...

### Problem 5 RStudio c) Must be able to put code where it says # Insert R code below this line

Let x be a random variable that represents white blood cells count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean ${\bf \mu}=7500$ and estimated standard deviation ${\bf \sigma}=1750$. A test result of $x < 3500$ is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.

a) What is the probability that, on a single test, x is less than 3500?

a) What is the probability that, on a single test, x is less than 3500?

```{r} # Insert R code below this lin# PART a) we have this one # Setting seed for find values set.seed(134) # Generating data when sample size = 42, mean = 2500, standard deviation is = 300 x <- rnorm(n = 42, mean = 2500, sd = 300) # Installing package fitdistrplus install.packages("fitdistrplus") # Loading the package library(fitdistrplus) # Checking if data is normally distributed normal_dist <- fitdist(x, 'norm') # Plotting the curve plot(normal_dist) # Graph below clearly shows that data is normally distributede

```

b) Suppose a doctor uses the average ${\bar x}$ for two tests taken about a week apart. What can we say about the probability distribution of ${\bar x}$? What is the probability of ${\bar x} < 3500?

```{r}

# Insert R code below this line # PART b) The probablity between two given values is subtracted to get the desired probability

# The probability comes out to be 0.38

pnorm(2650, mean = 2500, sd = 300) - pnorm(2350, mean = 2500, sd = 300) # we have this one too..

```

c) Repeat part b for $n = 3$ tests taken a week apart. ```{r} # Insert R code below this line need RStudio Solution not Java # we just need this answer to get 100%

```