Question

In: Statistics and Probability

Salaries for teachers in a particular elementary school district are normally distributed with a mean of...

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.

Solutions

Expert Solution

Given that, mean (μ) = $44000 and

standard deviation = $6500

X ~ N(44000, 6500)

We want to find, the value of x such that, P(X ≤ x) = 0.85

Therefore, the 85th percentile for the sum of the sampled teacher's salaries is $50736.80

Note : Using Excel we get, Z0.85 = 1.03643

Excel Command : =NORMSINV (0.85) = 1.03643

orchestra answered 2 years ago
Next > < Previous

Related Solutions

Salaries for teachers in a particular elementary school district are normally distributed with a mean of...
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...
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...
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 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...
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...
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. $ =
Salaries for teachers in a particular elementary school district are normally distributed with a mean of...
Salaries for teachers in a particular elementary school district are normally distributed with a mean of $44,000 and a standard deviation of $6,300. 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. A typical adult has an average IQ score of 105 with a standard deviation of 20. If 19 randomly selected adults are...
7.75 p. 428 Salaries for teachers in a particular elementary school district are normally distributed with...
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...
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...
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...
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...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT