Question

Suppose the average income of students as $100 per day with a standard deviation of $10 now a student is selected at random and the main income is $100 what is the value

Answer 1

The answer is below

Step-by-step explanation:

Suppose the average income of students is $100 per day with a standard deviation of $10 now a student selected at random and the main income is $100 what percentage of student incomes is below $100

Solution:

The z score is a score used in statistics to determine by how many standard deviations the raw score is above or below the mean score. If the raw score is above the mean score then the z score is positive while if the raw score is below the mean score the z score is negative.

The z score is given by:

`z=(x-\mu)/(\sigma) \\\\for\ a\ sample\ size(n)\ \\\\z=(x-\mu)/(\sigma/√(n) )`

Where μ is the mean, σ is the standard deviation and x the raw score.

Given that μ = 100, σ = 10. Hence:

For x < 100:

`z=(x-\mu)/(\sigma) =(100-100)/(10) =0\\\\`

From the normal distribution table, P(x < 100) = P(z < 0) = 0.5 = 50%