Statistics and Probability Answers

The data shown here represent the ages of patients who were found to have liver deficiency and weak lungs due to smoking and undergone several tests, and samples of urine were tested and examined immediately after the submission of specimen.

12 17 10 14 20 28
16 18 12 16 17 9
15 16 21 25 16 16
12 14 15 12 15 23
19 13 16 18 16 14

a. Construct a frequency distribution. ( i =3)

b. Construct a frequency polygon.

c. Construct a histogram

“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”.

Four of the Statistics for Business and Economics students submitted an entry to a Math contest at the faculty. A total of 24 entries were submitted. Six of the entries will move on to the next round. What is the hypergeometric probability that fewer Statistics for Business and Economics students than expected will make it to the next round?

Quantitative Methods Question:
a. The average rate of emission radioactive particles from a source was measured over a long period, and found to be 10 particles per unit time. After an experimental treatment had been applied to the source, a further sample was examined and emitted 17 particles in unit time.

Test at 5% the null hypothesis that the rate of emissions is unchanged.

A large number of automobile batteries have an average life length of 24 months. 34% of them have than a months, is average life between 22 and 26 months and 272 of them last longer than 29 months. If life of the batteries follows normal distribution, how many batteries were tested? What is the standard deviation?

Given that P(0<=3 <=0.44) = 0.17, P(0<=Z<=1.1) = 0.3643.

A machine elastic bands with breaking tension normally distributed with mean 45 N and standard deviation 4.36 N.
a. In order to test whether there is a change in the mean breaking tension, a random
sample of 50 was tested and found to have a mean breaking tension of 43.46 N.
i. Determine a 95% confidence interval for the population mean breaking tension
based on the sample mean assuming an unchanged standard deviation.

The average rate of emission radioactive particles from a source was measured over a long period, and found to be 10 particles per unit time. After an experimental treatment had been applied to the source, a further sample was examined and emitted 17 particles in unit time. Test at 5% the null hypothesis that the rate of emissions is unchanged.

The length,x centimeters,of eels in a river may be assumed to be normally distributed with mean 48 and standard deviation 8.An angler an eel from the river.Determine the probability that be length of the eel is : a) exactly 60 cm b) less than 60 cm c) within 5% of the mean length

An iron ball diameter measurement is installed automatically in a factory. The gauge will only pass the ball diameter of 1.50 ± d cm. It is known that the ball of the factory production has a diameter that is normally distributed with a mean diameter of 1.50 and a standard deviation of 0.2 cm. If it is desired that 95% of the production passes the selection, should the value be determined?

Say we have 14 people in this room; it was found there are 4 people having a height from
150 to 160 cm; 4 people having a height from 160 to 170 cm; 6 people having a height from 170 to 180 cm; what is the estimated height average in the class?