Statistics and Probability Answers

Three samples each of size 5 were drawn from 3 uncorrelated normal populations with equal variances. Analyse the hypothesis that the population means are equal at 5%level.
Sample-1
10
12
9
16
13

Sample-2
9
7
12
11
11

Sample-3
14
11
15
14
16

A minimum height is to be prescribed for eligibility to
government services such that 75.80% of the young men will have a
fair chance of coming up to that standard. The height of young
men is normally distributed with mean 62 inches and standard
deviation 3.5 inches. Determine the minimum specification.

“FunBakery” is a bakery shop that customers can use the facilities to bake cakes. According to the record, the duration a customer spends in the shop follows a normal distribution with mean 140 minutes and standard deviation 18 minutes.
(a) What is the probability that a customer stays in the shop for more than 3 hours?
(b) There are 15% of all customers would stay in the shop for less than t minutes. Find the value of t. Round
up the answer to the next integer.
The charge in “FunBakery” is $100 for the first hour and then $1.1 per extra minute.
(c) Find the average, median and standard deviation of the amount of money a customer spends in the shop.
(d) For a customer stays in the shop for 3 hours, how much he / she needs to pay?
(e) There are 15% of all customers would pay less than $k. Find the value of k by using your answer in
part (b).
(f) Write a simple summary about the spending of a customer in “FunBakery”.

the number of miles that Anita's motorbike will be travel on one gallon of petrol may be modelled by a normal distribution with mean 135 and standard deviation 12.a) given that Anita starts journey with one gallon of petrol in her motorbike's tank, find the probability that, without refeulling,she can travel.i) more than 111 miles,ii) between 141 and 150 miles.b) find the longest journey that Anita can undertake,if she is to have a probability of that at least 0.9 of completing it on one gallon of petrol

A researcher claims that a patient takes on the average 12.8 months to fully recover. Random sample of 60 patients were studied, the mean 11.2months and standard deviation of 3.5 month. Test the researcher’s claim at 0.01 level of significant

The life of a compressor manufactured by a company is known to be 200 months on an
average following an exponential distribution .Find the probability that the life of a
compressor is i) less than 200 months ii) between 100 months to 25 years.

The life of a compressor manufactured by a company is known to be 200 months on an
average following an exponential distribution .Find the probability that the life of a
compressor is i) less than 200 months ii) between 100 months to 25 years.

. The average weight of bags of maize meal packed at a particular farm is assumed to be normally distributed with a mean of 20 kg and a standard deviation of 3.0 kg. Determine the probability that a bag weighs between 19.5 kg and 22.0 kg?

diary company produces 188 milk containers in one hour. The quality team select 39% every hour and check if it passes the quality check. The probability of passing is 83%. The management is happy if the 77% of the sample passes. What the probability that makes the management happy.[

Consider a population of 6 units with values 1, 2, 3, 4, 5 and 6. Write down
all possible samples of size 2 from this population. Obtain the sampling
distribution of the sample mean. Compute mean and variance of the sampling
distribution obtained.