In: Physics

Salaries for teachers in a particular elementary school district are normally distributed with a mean of $46,000 and a standard deviation of $4,900. We randomly survey ten teachers from that district. (Round your answers to the nearest dollar.)

(a) Find the 90^{th} percentile for an individual
teacher's salary.

(b) Find the 90^{th} percentile for the average teacher's
salary.

let,

if a random sample of size n is drawn from the population, then as n increases, the random variable which consists of sample means, tends to be normally distributed and

According to central limit theorem for sample means or averages, when larger and larger samples are drawn from the population and their means are calculated, it is found that the sample means form their own normal distribution and the normal distribution has mean same as the original distribution and the variance equal to original variance divided by n.

(note: variance is the square of standard deviation)

The random variable has different values of z scores associated with it, which is given as follows:

where is the value of in one sample

Note that,

whereas,

and is given by

a) For an individual teacher's salary, the sample size is 1

The mean and standard deviation for the distribution are:

Now for calculating the 90th percentile, we use
**NORM.INV** function of **Excel** which
has format **NORM.INV(probability,mean,standard
deviation)**

Here, we have to calculate the 90th percentile for an individual teacher's salary, which indicates the salary below which 90% of the individual teachers fall.

Thus we have to find

we make the use of excel for finding value of Z

thus using **NORM.INV(probability,mean,standard deviation)
= NORM.INV(0.90,46000,4900)**, we get the required value of
salary as 52280 i.e $ 52,280

Thus the 90th percentile for individual teacher's salary is $ 52,280

b) For the average teacher's salary, the sample size is 10

Thus the mean and standard deviation for the distribution are:

Now using **NORM.INV** function of
**Excel** to calculate 90th percentile as in part
a),

**NORM.INV(probability,mean,standard deviation) =
NORM.INV(0.90,46000,1550)** we get required value of salary
as 47986 i.e $ 47,986

Thus the 90th percentile for the average teacher's salary is $ 47,986.

Salaries for teachers in a particular elementary school district
are normally distributed with a mean of $44,000 and a
standard deviation of $6,500. We randomly survey ten teachers from
that district.
1.Find the probability that the teachers earn a total of over
$400,000
2.If we surveyed 70 teachers instead of ten, graphically, how
would that change the distribution in part d?
3.If each of the 70 teachers received a $3,000 raise,
graphically, how would that change the distribution in part...

Salaries for teachers in a particular elementary school district
are normally distributed with a mean of $44,000 and a standard
deviation of $6,500. We randomly survey ten teachers from that
district. Find the 85th percentile for the sum of the sampled
teacher's salaries to 2 decimal places.

Salaries for teachers in a particular elementary school district
are normally distributed with a mean of $41,000 and a standard
deviation of $6,100. We randomly survey ten teachers from that
district.
A. Give the distribution of ΣX. (Round your answers to
two decimal places.)
ΣX - N ( , )
B. Find the probability that the teachers earn a total
of over $400,000. (Round your answer to four decimal places.)
C. Find the 80th percentile for an individual
teacher's salary....

Salaries for teachers in a particular elementary school district
are normally distributed with a mean of $46,000 and a standard
deviation of $4,500. We randomly survey ten teachers from that
district. (Round your answers to the nearest dollar.)
A) Find the 90th percentile for an individual
teacher's salary.
B)Find the 90th percentile for the average teacher's
salary.

Salaries for teachers in a particular elementary school district
are normally distributed with a mean of $42,000 and a standard
deviation of $5,700. We randomly survey ten teachers from that
district. (Round your answers to the nearest dollar.)
(a) Find the 90th percentile for an individual
teacher's salary.
$ =
(b) Find the 90th percentile for the average teacher's
salary.
$ =

7.75 p. 428
Salaries for teachers in a particular
elementary school district are normally distributed with a mean of
$44,000 and a standard deviation of $6,500. We randomly survey ten
teachers from that district.
a. In words, X = ______________
b. X ~ _____(_____,_____)
c. In words, ΣX = _____________
d. ΣX ~ _____(_____,_____)
e. Find the probability that the
teachers earn a total of over $400,000.
f. Find the 90th percentile for an
individual teacher's salary.
g. Find the...

Salaries for teachers in a particular elementary school district
have a mean of $44,000 and a standard deviation of $6,500. We
randomly survey 36 teachers from that district.
Why can we say the sampling distribution of mean salaries for
teachers in this district is approximately normal?
Find the probability that the mean salary is less than
$43,000.
Find the probability that the mean salary is between $45,000
and $47,000.

A researcher claims that the mean of the salaries of elementary
school teachers is greater than the mean of the salaries of
secondary school teachers in a large school district. The mean of
the salaries of a random sample of 26 elementary school teachers is
$48,250 and the sample standard deviation is $3900. The mean of the
salaries of 24 randomly selected secondary school teachers is
$45,630 with a sample standard deviation of $5530. At ? = 0.05, can
it...

A study was conducted to estimate the difference in the mean
salaries of elementary school teachers from two neighboring states.
A sample of 10 teachers from the Indiana had a mean salary of
$28,900 with a standard deviation of $2300. A sample of 14 teachers
from Michigan had a mean salary of $30,300 with a standard
deviation of $2100. Determine a 95% confidence interval for the
difference between the mean salary in Indiana and Michigan.(Assume
population variances are different.)
*Include...

A researcher claims that the variation in the salaries of
elementary school teachers is greater than the variation in the
salaries of secondary school teachers. A random sample of the
salaries of 30 elementary school teachers has a variance of $8,208,
and a random sample of the salaries of 30 secondary school teachers
has a variance of $3,817. At α = 0.05, can the researcher conclude
that the variation in the elementary school teachers’ salaries is
greater than the variation...

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