Question

Teacher salaries for a particular district are known to have a normal distribution

with a mean of $38,500 and a standard deviation of $880.

a)What is the probability that a randomly chosen teacher from this district makes less than $41,000?

b)What is the probability that a randomly chosen teacher from this district makes more than $37,000?

c)What is the probability that a randomly chosen teacher from this district has a salary between $36,000 and $38,000.

d)One veteran teacher comments that her salary is at the 95th percentile for the district. What is her salary?

Answer #1

Solution :

Given that,

mean = = 38,500

standard deviation = = 880

a ) P( x < 41,000 )

P ( x - / ) < ( 41,000 - 38,500 / 880)

P ( z < 2500 / 880 )

P ( z < 2.84)

= 0.9977

Probability =0.9977

b ) P (x > 37,000 )

= 1 - P (x < 37,000 )

= 1 - P ( x - / ) < ( 37,000- 38,500 / 880)

= 1 - P ( z <- 1500 / 880 )

= 1 - P ( z < -1.70)

Using z table

= 1 - 0.0446

= 0.9554

Probability = 0.9554

c ) P (36,000 < x < 38,000 )

P ( 36,000 - 38,500 / 880) < ( x - / ) < ( 38,000 - 38,500 / 880)

P ( - 2500 / 880 < z < -500 / 880 )

P (-2.84 < z < - 0.57)

P ( z < - 0.57 ) - P ( z < -2.84)

Using z table

= 0.2843 - 0.0023

= 0.2821

Probability = 0.2821

d ) P(Z < z) = 95%

= P(Z < z) = 0.95

= P(Z < -0.6745 ) = 0.95

z = 1.64

Using z-score formula,

x = z * +

x = 1.64 * 880 + 38,500

x = 39943.2

Salaries for teachers in a particular elementary school district
are normally distributed with a mean of $45,000 and a standard
deviation of $6,100. 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 $44,000 and a standard
deviation of $6,500. We randomly survey ten teachers from that
district. Using Excel and the functions, show me how you
got your answer
Find the 90th percentile for an individual teacher’s
salary.
Find the 90th percentile for the average teacher’s
salary.

75.
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.
In words, X = ______________
X ~ _____(_____,_____)
In words, ΣX = _____________
ΣX ~ _____(_____,_____)
Find the probability that the teachers earn a total of over
$400,000.
Find the 90th percentile for an individual teacher's
salary.
Find the 90th percentile for the sum of ten
teachers' salary....

The life of a particular battery is known to follow a normal
distribution , with a mean of 1264 hours and a standard deviation
of 116 hours.
a. What percent of batteries last less than 1511 hours?
0.98341425
b. The 95 th percentile is represented by what number of hours
of battery life?
c. What is the probability that a randomly selected battery will
last more than 1154 hours? 0.17156471
Incorrect

The average yearly salary of RN’s is $70,000. If the
distribution of salaries is
approximately normal with a standard deviation of $5,000,what is
the probability that
a randomly selected RN makes:
Between $60,000 and $70,000 a year.
More than $70,000 a year.

The average teacher’s salary is $45,000. Assume a normal
distribution with standard deviation equal to $10,000. a) What is
the probability that a randomly selected teacher makes greater than
$65,000 a year? b) If we sample 100 teachers’ salaries, what is the
probability that the sample mean will be greater than $65,000?

[5] 3. The
average teacher’s salary is $45,000. Assume a normal distribution
with standard
deviation equal to $10,000.
What is the probability that a randomly selected teacher makes
greater than $65,000 a year?
If we sample 100 teachers’ salaries, what is the probability
that the sample mean will be greater than $65,000?

The average teachers' salary in a certain state is $57,337.
Suppose that the distribution of salaries is normal with a standard
deviation of $7500. Assume that the sample is taken from a large
population and the correction factor can be ignored. Use a TI-83
Plus/TI-84 Plus calculator and round the answer to at least four
decimal places.
What is the probability that a randomly selected teacher makes
less than $51,000 per year?

The average teacher's salary in Connecticut (ranked first among
states) is $57,337. Suppose that the distribution of salaries is
normal with a standard deviation of $7500.What is the probability
that a randomly selected teacher makes less than $49,000 per
year?

The annual salaries of College Presidents in 1993 had a
population mean of $150,000 and standard deviation of $20,000. A
random sample of 64 College Presidents is chosen from this
population. 11. What is the probability that the sample average
salary of this randomly chosen sample is less than $144,300? a.
0.0113 b. 0.0222 c. 0.0375 d. 0.4778 e. 0.6293

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 23 minutes ago

asked 24 minutes ago

asked 25 minutes ago

asked 36 minutes ago

asked 37 minutes ago

asked 47 minutes ago

asked 51 minutes ago

asked 51 minutes ago

asked 52 minutes ago

asked 57 minutes ago

asked 1 hour ago