Statistics and Probability- Sample questions

1. a. The table below shows the distribution of the brand of cars that play on a given road in a week

Brand
of cars
MazdaHyundai FordToyota NissanKIABenz
Frequency 1432261810134

i. Draw a bar chart for the data.

ii. What is the modal brand of car?

iii. The modal brand of car and Toyota constitute what percentage of cars?

b. A pair of six-sided die are rolled once and the number that show up are added to make a score:

i. Display the sample space in a table

ii. Find the probability that the sum of the numbers that show up on the two dice is;

a) odd

b) six or ten

c) a multiple of 2

2. The following are the scores obtained by students in a class test.

2 5 3 5 9 3 4 2 6 4 7 5

6 4 5 8 6 4 6 5 7 3 5 9

9 4 5 6 3 5 5 8 6 4 2 6

5 5 7 6 5 4 7 5 5 8

a. Prepare a frequency distribution table for the data.

b. Calculate the mean score, correct to one decimal place.

c. Calculate the standard deviation, correct to one decimal place.

d. If a student is selected at random from this group, find the probability that

i. his score is greater than or equal to 2 but more than 5

ii. his score is a prime number.

3. a. Mr. Karim was to supervise the distribution of beans to disaster victims in a town in the North. The bag of beans may be large or medium and the type may be white, red, or brown.

The table below shows the distribution of 500 bags of beans.

Type/SizeWhiteRedBrownTotal
Large95220
Medium 130
Total180120500

i. Copy and complete the table

ii. If a bag of beans is picked at random, find the probability that it is

a) red and large;

b) red

c) red and medium

iii. If a bag of beans picked at random is found to be large, what is the probability that it is brown?

b. Given that the mean of 19, (┬Ży), (2y-3) and 20 is 10, find y.

4. The distribution of ages of adults who visited a hospital is shown in the table below.

Age45-4950-5455-5960-6465-6970-7475-7980-84
Frequency 1921272315758

a. Prepare a cumulative frequency table.

b. Use your table to draw a cumulative frequency curve for the data.

c. Find the semi-interquartile range from your curve

d. If 15% of the students had distinction, what is the minimum mark for the distinction?

5. The mark distribution for a test is displayed in a grouped frequency table below.

Mark1-910-1920-2930-3940-49
Frequency 4718156

i. Calculate the standard deviation

ii. What is the probability that a student selected at random obtained a score of more than 29?

b. Mr. Bawa tossed two fair coins and a fair die together once, in an experiment involving a toss of coins and a die. Find:

i. the sample space;

ii. the probability that at least on tail will show on the coins and a prime number on the die.a

Qweku Styles

Mommy and Daddy call me Chris. Colleagues call me Osei and more recent friends call me Kuffour. I choose both mom and dad as my favorite. I am a writer and freelancer. I happily share my experiences crisscrossing on social media. Follow us: Facebook: Legacynewsgh Twitter: @Alpha_Qweku Instagram: QwekuStyles WhatsApp: 0561354834/0593725660

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