Step 1: Do on paper by hand using the Z score formula and scan or take a snapshot of all steps of your work.

1. Drug Dosage in Pharmaceutical Science

A pharmaceutical company is developing a new drug and wants to ensure that the drug's concentration in the blood follows a normal distribution. Clinical trials have shown that the concentration of the drug in the blood after one hour follows a normal distribution with a mean of 75 mg/L and a standard deviation of 10 mg/L.

1. What percentage of patients will have a concentration of the drug between 65 mg/L and 85 mg/L?
2. If the company wants to ensure that only 5% of the patients have a concentration above 95 mg/L, what concentration should they use as a threshold?

Step 2: Do the following work in SAS (include any graphs required in the assignment)

1. Healthcare Analytics and Patient Blood Pressure

A new drug aimed at lowering cholesterol was tested on 1,000 patients. The cholesterol reductions (in mg/dL) were found to be normally distributed with a mean of 50 mg/dL and a standard deviation of 10 mg/dL.

1. Generate a normally distributed dataset in SAS for the following parameters:
   • Mean: 50 mg/dL
   • Standard Deviation: 10 mg/dL
   • Sample Size: 1,000

%let sample_size = 1000;

%let mean = 50;

%let std_dev = 10;

data normal_data;

call streaminit(123); /* Sets seed for reproducibility */

do id = 1 to &sample_size;

concentration = rand("NORMAL", &mean, &std_dev);

output;

end;

run;

/* View summary statistics to verify */

proc means data=normal_data mean std min max;

var concentration;

run;

/* Optional: Visualize distribution */

proc sgplot data=normal_data;

histogram concentration / scale=count;

density concentration / type=normal mu=&mean sigma=&std_dev;

title "Histogram of Normally Distributed Drug Concentration";

run;

B. Plot the normal distribution of cholesterol reduction using SAS.

/* Step 1: Create a dataset with simulated normal values */

data cholesterol_reduction;

call streaminit(123); /* Set seed for reproducibility */

do id = 1 to 1000;

reduction = rand("NORMAL", 50, 10); /* mean = 50, std dev = 10 */

output;

end;

run;

/* Step 2: Plot histogram with normal density curve overlay */

proc sgplot data=cholesterol_reduction;

histogram reduction / scale=percent binwidth=2;

density reduction / type=normal; /* Removed mu= and sigma= */

title "Normal Distribution of Cholesterol Reduction";

xaxis label="Cholesterol Reduction (mg/dL)";

yaxis label="Percentage of Patients";

run;

C. What percentage of patients experienced a cholesterol reduction between 40 and 60 mg/dL?

data cholesterol_range;

/* Parameters */

mean = 50;

std_dev = 10;

/* Cumulative probabilities */

p_lower = cdf('NORMAL', 40, mean, std_dev); /* P(X <= 40) */

p_upper = cdf('NORMAL', 60, mean, std_dev); /* P(X <= 60) */

/* Percentage between 40 and 60 */

percentage_between = (p_upper - p_lower) * 100;

put "Percentage of patients with cholesterol reduction between 40 and 60 mg/dL = " percentage_between 6.2 "%";

run;

D. If a reduction of 70 mg/dL or more is considered a "significant" result, what proportion of patients achieved this threshold? (This is a greater than question)

Code for Crop yield example (Not on powerpoint):

/* Calculate the proportion of plants with yield increase of 100 kg/ha or more */ data proportion_significant; /* Calculate the z-score for 100 kg/ha */ threshold = 100; /* Calculate cumulative probability for the threshold */ p_threshold = probnorm((threshold - &mean) / &std_dev);

/* Calculate the proportion of plants exceeding the threshold */ proportion_exceeding = 1 - p_threshold; /* Proportion that exceeds the threshold */ percentage_increase = (proportion_exceeding) * 100; /* Convert to percentage */ run;

/* Display the results */ proc print data=proportion_significant noobs; var percentage_increase; label percentage_increase = "Proportion of Plants (100 kg/ha or more)"; run;

E. What implications do these findings have for determining the drug's effectiveness?

What you need to submit: (1) Write out the answers for questions 1 (Step 1). (2) On same document, paste your the full SAS code used to generate the dataset and plot the graph. (3) Include the normal distribution graph generated in SAS for the scenario. (4) Provide detailed answers to the analysis questions for the scenario.