Instruction 6-4 John Has Two Jobs.For Daytime Work at a Jewelry Store

question 65

Short Answer

Instruction 6-4
John has two jobs.For daytime work at a jewelry store he is paid $15,000 per month,plus a commission.His monthly commission is normally distributed with mean $10,000 and standard deviation $2,000.At night he works as a waiter,for which his monthly income is normally distributed with mean $1,000 and standard deviation $300.John's income levels from these two sources are independent of each other.
-Referring to Instruction 6-4,for a given month,what is the probability that John's income as a waiter is no more than $300?

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Definitions:

Two Normally Distributed Populations

Refers to two groups or populations where the data points follow a normal distribution, with specific means and standard deviations.

Independent Samples

Two or more samples that are collected from populations, or groups, that do not affect one another and have no relationship between them.

Pooled Variance Estimate

A method to estimate variance combined from two or more samples that assumes the samples originate from populations with the same variance.

Common Variance

The variance shared by two or more variables, often assessed to understand the relationship or correlation between them.