Class 12 CBSE Applied Maths Probability Exercise 9.6

Class 12 CBSE Applied Maths aims to develop an understanding of basic mathematical and statistical tools and their applications in the field of commerce (business/ finance/economics) and social sciences. Topics covered in Class 12th Applied Maths includes : Numbers, Quantification and Numerical Applications, Algebra, Calculus, Probability Distributions , Inferential Statistics, Index Numbers and Time-based data , Financial Mathematics , Linear Programming.


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Exercise 9.1 Exercise 9.2 Exercise 9.3 Exercise 9.4 Exercise 9.5

Q1.If Z is a standard normal variable, find each of the following probabilities:

(i) P(Z < 1.9)
(ii) P(Z>2.7)
(iii) P(Z<-0.84)
(iv) P(0< Z< 1.45)
(v) P(Z>-0.57)
(vi) P(-1.3< Z< 2.4)
(vii) P(1.8< Z< 2.9)
(viii) P(-3.01 < Z<-1.38)

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Q2.If X is a normal distribution random variable with mean 12 and standard deviation 3, find each of the following probabilities:

(i) P(X< 15)
(ii) P(X ≥18)
(iii) P(X< 9)
(iv) P(X>6)
(v) P(12< X< 21)

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Q3.Given Zis a standard normal random variable, find Z for each of the following:

(i) The area to the left of Z is 0.9750
(ii) The area between 0 and Z is 0.4750
(iii) The area to the right of Z is 0.1314
(iv) The area to the right of Z is 0.3300
(v) The area between -Z and Z is 0.9030.

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Q4.For a certain type of laptops the charging time of batteries is normally distributed with mean 50 hours and standard deviation 15 hours. Utkarsh has one of these laptops. Find the probability that the charging time of battery will be between 50 and 70 hours.

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Q5.The lifetime of an item produced by a machine is normally distributed with mean 12 months and standard deviation 2 months. Find the probability that an item produced by this machine will last

(i) less than 7 months
(ii) between 7 and 12 months
(iii) more than 14 months.

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Q6.If the heights of 1000 students are normally distributed with mean 173 cm and standard deviation 7.5 cm, how many students have heights

(i) greater than 183 cm?
(ii) less than 162.5 cm?
(iii) between 165 cm and 180 cm?

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Q7.The monthly salaries of 500 employees of a company are normally distributed with mean ₹10000 and standard deviation ₹1500. How many employees have salaries

(i) less than ₹8000?
(ii) more than ₹13000?
(iii) between ₹9000 and ₹14500?

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Q8.A radar unit is installed to measure the speeds of cars on a highway. The speeds are normally distributed with mean 80 km/h and standard deviation 10 km/h. If a car is chosen at random, find the probability that car is running

(i) at less than 60 km/h

(ii) at more than 100 km/h
(iii) between 90 km/h and 110 km/h.

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Q9.The test scores of university entrance test are normally distributed with mean 500 marks and standard deviation 100 marks. A student can get admission if he scored marks better than atleast 70% students. A student is selected at random and known to have a score of 585 marks. Find whether the student will get admission in the university or not.

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Q10.In a car manufacturing plant, the time taken to assemble a car is normally distributed with mean 18 hours and standard deviation 1.5 hours. If a car manufactured in that plant is selected at random, find the probability that it is assembled in

(i) less than 16 hours
(ii) more than 19 hours
(iii) between 18 hours to 21 hours.

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Q11.The monthly salaries of workers in a certain factory are normally distributed with mean ₹5000 and standard deviation ₹500. There are 14 workers getting more than ₹6500 per month. Find the total number of workers in the factory.

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Q12. If X is normally distributed with mean 10 and standard deviation 1.5, find x such that P(X>x)=0.0038.

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Q13. A company conducted an I.Q. test for randomly selected 50 employees. Volunteer A scored 74 out of the possible 120 points. If the average I.Q. test score was recorded as 62 and the standard deviation was 11. How well did volunteer A perform in the test as compared to the other volunteers?

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Q14.On an average, ceiling fan manufactured by Jagdeep Corporation lasts 300 days with a standard deviation of 50 days. Assuming that the ceiling fans life is normally distributed, what is the probability that a ceiling fan will last atmost 365 days

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