Question

High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 18 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized? (Round your answer to 2 decimal places.)

Need in text format no handwriting thank u

Answer 1

SOLUTION:

From the Given data

High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam.

Let us assume a Students Score “X " has a normal distribution

X ~ N (μ, σ )

Where μ = population mean

           σ = standard deviation

So ‘X’ is the random variable which represent the score obtained by a student in the Examination

Let X₁ be the score beyond which 0.18 of area

Now to calculate the Z score at X₁

P (X > X₁) = 0.18

Here the Z- score corresponding the area of 0.18 is given by Z = 0.92 ( by using the z table )

P (X > 0.92) =0.18

We have to search for the 0.18 value in the z table under the column 0.02 and 0.9 row

Value lies between 0.91 and 0.92 we consider 0.92 which is very near to 0.18

by seeing the table we got the value corresponding to the area