Answer:
1) $42,012
2) 0.34134
3) 0.47725
4) $34,173
5) 0.02275
6) Yes, it is likely
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