Statistics and Probability Answers

What is the probability that a child, picked at a random, has a greater than 116 cm?

a manufacturer of light bulbs produces bulbs that last a mean of 950 hours with a standard deviation of 12 hours what is the probability that the mean lifetime of the random sample of 10 of these bulbs is less than 90 hours

Assume the population is normally distributed with: 

Xbar = 96.44           S =10.2        n=15                 t=1.76

Construct a​ 90% confidence interval estimate for the population​ mean, μ

what is the difference between z value vs t value?

In a random sample of 500 observations drawn from a normal population, the sample mean and sample standard deviation were calculated as X =350 and s = 100.

a) Estimate the population mean with 99% confidence.

b) Repeat part (a) assuming that you know that the population standard deviation is  = 100.

c) Explain why the interval estimates were virtually identical. 

Two dice are tossed. Find the probability of getting ‘an even number on the first dice or a 

total of 8 ‘.

The monthly returns for the period July 1996 to May 2001 for United Kingdom and

Australian index were recorded. Determine the regression line and interpret the coefficients.

Sample statistics,

n=59  SSx=0.0931  SSxy=0.04817  SSy=0.793

x̅ uk=0.008175  y̅aus=0.007891

A research was conducted in 2017 at the Tema Port to find the ages of cars imported into 

the country. According to the research, 10% of the cars imported were less than one-year￾old. Assuming this result holds true for the current period for all cars imported into the 

country.

Find the probability that in a random sample of 5 cars at the Tema Port

(i) exactly 3 are less than one-year-old.

(ii) exactly 2 are less than one-year-old.

(iii) none is less than one-year-old 

(iv) Find the mean and standard deviation of the distrib

A population consists of the following measurement 3,8,14,17, and 58 consider all the sample of size 3 taken from this population without replacement

(1)List the sample of the mean and media respectively

(2) calculate the mean of the sample distribution of the media and the means

 A charity group raises funds by collecting waste paper. A skip-full will contain an 

amount, X, of other materials such as plastic bags and rubber bands. X may be regarded 

as a random variable with probability function

𝑓(𝑥) = {𝑘(𝑥 − 1)(4 − 𝑥) , 1 < 𝑥 < 4

0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

 (All numerical values in this question are in units of 100kg,)

i )Show that 𝑘 =1/2.

 ii)Find the mean and the standard deviation of X.