Statistics and Probability Answers

Assuming the standard deviation is unchanged and that the usage is normally distributed, provide an expression for calculating a 99% confidence interval for the mean usage in the March quarter of 2006. (Exactly one option must be correct)

A random sample of 60 Grade 11 students’ ages is obtained to estimate the mean ages of all Grade 11 students. Suppose the sample mean is 17.3 and the population variance is 18,

What is the point estimate of the population parameter?

Find the 95% confidence interval for the population parameter?

Find the 99% confidence interval for the population parameter?

= 82.5; s = 3. The parent population is normally distributed. Use the 95% confidence level to find the interval estimate for µ.

Height Frequency

 ( to nearest cm)

 150-159 11

160-169 24

170-179 21

180-189 15

a. State any assumption you make if calculating the mean and standard deviation for this data sample.​

b. State the boundaries and the class limits for the class interval containing the median. ​​

c. Which is the modal class interval and why?​

d. Calculate an estimate for the mean height.​

e. Calculate an estimate for the standard deviation.

What is the value of the finite population correction factor in the formula for o when

n=100 and N = 5000.

The annual dollar value of homes sold by real estate salespersons in a certain

community has a mean of $7.5 million, with a standard deviation of $4.4 million.

Find the probability that, in a random sample of 36 such salespersons, the sample

mean annual dollar value of homes sold will

(i) be less than $6.5 million; [2 marks]

(ii) exceed $9.0 million.

The income of brokers in Barbados is normally distributed. A sample of 54 brokers has an

average yearly income of BD$86,000 with standard deviation of BD$12,000. Find the

98% confidence interval for the yearly mean income of Barbadian brokers.

Michael is a delivery man for a pizza chain. He has 14 late deliveries out of 45 on

Sunday. The manager’s policy requires him to fire a delivery man if his rate of late

deliveries is above 0.2. Conduct a test at the 5% level of significance to determine if the

manager will fire Michael.

Given the function

𝑥

3 − 13𝑥

2

+ 25𝑥 + 25 = 0

(a) Show that the equation has a root in the interval (− 2, 2).

(b) Use 2 iterations of Newton’s method to find an approximation for this root.

(c) Use 2 iterations of the bisection method to find an approximation for this

root.

if a letter is chosen at random from the 10 letters of the word statistics wat is probability that it is a vowel?

For instance, one of your friends from another school asks your help about his problem in Statistics and

Probability. He needs to answer his assignment but unfortunately, he left his module in the school

. He wants

to know how to identify the regions under the normal curve corresponding to different standard normal values.

Your friend will send a picture of a normal curve with the corresponding area, and he asks you favor to explain

each picture on how to obtain the value of the shaded part of the normal curves. Here is the screenshot of the

pictures