Homework Answers

City planners wish to estimate the mean lifetime of the most commonly planted trees in urban settings. A sample of 16 recently felled trees yielded mean age 32.7 years with standard deviation 3.1 years. Assuming the lifetimes of all such trees are normally distributed, construct a 99.8% confidence interval for the mean lifetime of all such trees.

A random sample is drawn from a normally distributed population of known standard deviation 5. Construct a 99.8% confidence interval for the population mean based on the information given (not all of the information given need be used).

a. n = 16, 𝑥̅= 98, 𝑠 = 5.6

b. n = 9, 𝑥̅= 98, 𝑠 = 5.6

A government agency was charged by the legislature with estimating the length of time it takes citizens to fill out various forms. Two hundred randomly selected adults were timed as they filled out a particular form. The times required had mean 12.8 minutes with standard deviation 1.7 minutes. Construct a 90% confidence interval for the mean time taken for all adults to fill out this form.

A random sample of size 144 is drawn from a population whose distribution, mean, and standard deviation are all unknown. The summary statistics are 𝑥̅= 58.2 and s = 2.6.

a. Construct an 80% confidence interval for the population mean μ.

b. Construct a 90% confidence interval for the population mean μ.

compute the surface area generated when the first quadrant portion of the curve x^2-4y=8 from x1=0 to x2= 2 is revolved about the y-axis

A random sample is drawn from a population of known standard deviation 11.3.

Construct a 90% confidence interval for the population mean based on the information

given (not all of the information given need be used).

a. n = 36, 𝑥̅= 105.2, 𝑠 = 11.2

b. n = 100, 𝑥̅= 105.2, 𝑠 = 11.2

Compute the population proportion interval estimate given n, p, and the confidence level

a. Confidence Level= 99%, p=0.4, n=40

b. Confidence Level= 90%, p=0.15, n=55

A question in Probability & Statics:-

At a checkout counter, customers arrive at an average of 1.5

per minute. Assuming poisson distribution

1- The probability of no arrival in two minutes is.....

2- The variance of the number of arrivals in two minutes

is.....

3- Suppose X has binomial distribution with n=1000 and p

=0.002 , Then P(x=3)=....

A secretary makes 2 errors per page on the average. What is the probability that on the next 

page she makes; 4 or more errors and no error?

Let X be a random variable with probability distribution

X -1 0 1 2 3

F(X) 0.125 .50 0.20 0.05 0.125

a) Find E(X) and VAR(X).

b) Find the probability distribution of the random variable Y= 2X+1. Using the 

probability distribution of Y determine E(Y) and VAR(Y).