Assume that the data in each of the following problems is normally distributed. The average salary for a first-year teacher is $35,512 with a standard deviation of $3250. what salary is two standard deviations above the mean (average) salary?

what is the probability when a first-year teacher makes a salary between $35512 and $38762 ?

what's the probability that a first-year teacher makes a salary between $35,512 and $42,012?

what's salary range accounts for 34% of the salaries below the average salary?

what is the probability of a first-year teacher making more than $42,012

according to the data above, is it likely that a first-year teacher will make more than $46,000? explain your reasoning ​

1) $42,012

2) 0.34134

3) 0.47725

4) $34,173

5) 0.02275

6) Yes, it is likely

Step-by-step explanation:

We solve the above question using z score formula

z = (x-μ)/σ, where

x is the raw score

μ is the population mean = $35,512

σ is the population standard deviation = $3250

1) what salary is two standard deviations above the mean (average) salary?

Two standard deviations above the mean, the formula is given as:

μ + 2σ

$35,512 + 2 × $3250

= $42,012

Therefore, the salary that is two standard deviations above the mean (average) salary is $42,012

2) what is the probability when a first-year teacher makes a salary between $35512 and $38762 ?

For x = $35512

z = 35512 - 35512/3250

z = 0

Probability value from Z-Table:

P(x = 35512) = 0.5

For x = $38762

z = 38762 - 35512/3250

z = 1

Probability value from Z-Table:

P(x = 38762) = 0.84134

Hence, the probability when a first-year teacher makes a salary between $35512 and $38762 is calculated as:

P(x = 38762) - P(x = 35512)

0.84134 - 0.5

= 0.34134

3) what's the probability that a first-year teacher makes a salary between $35,512 and $42,012?

For x = $35512

z = 35512 - 35512/3250

z = 0

Probability value from Z-Table:

P(x = 35512) = 0.5

For x = $42012

z = 42012 - 35512/3250

z = 2

Probability value from Z-Table:

P(x = 42012) = 0.97725

Hence, the probability when a first-year teacher makes a salary between $35512 and $42012 is calculated as:

P(x = 42012) - P(x = 35512)

0.97725 - 0.5

= 0.47725

4) what's salary range accounts for 34% of the salaries below the average salary?

We find the z score of the 34th percentile

= -0.412

x is the raw score = ?

μ is the population mean = $35,512

σ is the population standard deviation = $3250

z = -0.412

Hence:

-0.412 = x - 35512/3250

Cross Multiply

-0.412 × 3250 = x - 35512

+ 1339 = x - 35512

x = 35512 - 1339

x = 34173

Therefore, the salary range accounts for 34% of the salaries below the average salary is $34,173

5) what is the probability of a first-year teacher making more than $42,012

More than = Greater than = >

For x >$42012

z = 42012 - 35512/3250

z = 2

Probability value from Z-Table:

P(x<42012) = 0.97725

P(x>42012) = 1 - P(x<42012)

= 0.02275

6).according to the data above, is it likely that a first-year teacher will make more than $46,000?

More than = Greater than = >

For x > $46,000

z = 46000 - 35512/3250

z = 3.22708

Probability value from Z-Table:

P(x<46000) = 0.99937

P(x>46000) = 1 - P(x<46000)

= 0.00062531

From the above calculations, yes, it is likely

Yes

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square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743