If X Is a Normal Random Variable with a Mean $P ( X \geq 50 )$

question 66

Essay

If X is a normal random variable with a mean of 45 and a standard deviation of 8, find the following probabilities:
a. $P ( X \geq 50 )$
b. $P ( X \leq 32 )$
c. $P ( 37 \leq X \leq 48 )$
d. $P ( 50 \leq X \leq 60 )$
e. $P ( X = 45 )$

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Definitions:

Assessed

Evaluated or estimated the nature, ability, or quality of something or someone, often used in contexts of taxation, education, and healthcare.

Fine-gauge Needle

A very thin needle used for injections, drawing blood, or administering medication, minimizing discomfort and tissue damage.

Dilute Solutions

Mixtures where a solute (such as a salt or a chemical) is dissolved in a solvent (like water) at a low concentration.

Allergens

Substances that are recognized by the immune system and can cause an allergic reaction in susceptible individuals.