Statistics and Probability Answers

the average cholesterol content of a certain canned goods is 215 milligram and the standard deviation is 15 milligram, answer the variable is normally distributed

In a shooting competition, Mr X can shoot at the bulls eye 4 times out of 5 shots and

Mr Y, 5 times out of six and Mr Z, 3 times out of 4 shots. Find the probability that

the target will be hit at least twice?

a normally distributed population has mean 57.7 and standard deviation 12.1

a) find the probability that a single randomly selected element x of the population is less than 45

b) find the mean and the standard deviation of x-x for sample size 16

c) find the probability that the mean of sample of size 16 drawn from the population is less than 45

The table below shows whether students from a certain University in Pretoria are right- or left- handed by sex. The total number of students who were interviewed was 100. Their responses were as follows:

    Right handed Left handed Total

Male Female 38 42

12 8

50 50

Total 80 20 100

      3.1.1 What is the probability of selecting a left-handed male? 3.1.2 What is the probability of selecting a right-handed female?

(5) (5)

n more than 75sec (5)

2.2 If it is estimated that 30% of all students who fall under the Business Economics and Management Department at Richfield have a valid driver’s license. What is the probability of this in a sample of 10 students?

2.2.1 Exactly 4 have a valid driver’s license? (5) 2.2.2 At least 2 have a valid driver’s license? (5) 2.2.3 More than 9 have a valid driver’s license? 

The head of the math department claims that the mean height of grade 7 students is 163 cm. the mean height of randomly selected grade 7 students is 161 cm. using 0.05 significance level can it be concluded that the mean height of grade 7 students is shorter than 163 cm?

A box contains 5 red balls, 6 white balls and 9 black balls. Two balls are drawn at random. (The first ball is not replaced). Find the probability that both balls are of the same colour.

Suppose the manufacturer’s specifications for the length of a certain type of computer cable are 1000 ± 10 millimeters. It is known that small cable is just as likely to be defective as large cable. That is, the probability of randomly producing a cable with length exceeding 1010 millimeters is equal to the probability of producing a cable with length smaller than 990 millimeters. The probability that the production procedure meets specifications is known to be 0.97.

The following table shows the sale of mobiles by a company in different months. Fit a trend line using any statistical software to this sales data. Make suitable assumptions.

Month Jan Feb Mar Apr May Jun July

Sales (in No of Units) 2000 1900 1950 1800 1600 1600 1800

Weight of students of a class having 40 student was recorded. This data is given in the following table. Perform the tasks given in (i) to (iv) on the data given below using a spreadsheet package: (6 Marks)

(Weight in Kgs)

42 54 60 55 49 46 55 38 65 40

61 46 47 42 51 53 59 57 46 60

52 54 50 60 58 44 49 39 48 56

47 53 52 57 55 44 51 47 61 43

(i) Find the minimum and maximum weight using the spreadsheet formula.

(ii) Create 6 classes with suitable class intervals and create the frequency distribution.

You must use Array formula.

(iii) Find the percentage of the students whose weight is less than the mean weight

(iv) Draw the histogram for the data above. Also try to relate it to normal distribution

curve.