## Normal Distribution Questions and Solutions

2021 April Q. No. 5a – 7.5 Marks

The average daily sale of 500 branch offices was Rs 100 thousand and the standard deviation Rs 10 thousand. Assuming the distribution to be normal indicate how many branches have sales (i) less than Rs 95 thousand, (ii)between Rs 75 thousand to Rs 110 thousand and (iii) between Rs 110 thousand toRs 130 thousand.

2012 April (back)-QN 5b

Sharma’s trucking company determined that the distance travelled by truck per year is normally distributed, with a mean of 50thousand miles and a standard deviation of 12 thousand miles.

i.What proportion of trucks can be expected to travel between 34 and 50 thousand miles in a year?

ii. What percentage of trucks can be expected to travel either less than 30 or more than 60 thousand miles in a year

2019 August Q. No. 5a- 7.5 Marks

Incomes of a group of 10,000 persons were found to be normally distributed with mean Rs. 52,000and standard deviation of Rs. 6,000. Find(i) the number of persons having income between Rs. 40,000 and Rs. 55,000 (i) the lowest income of the richest 1,000 persons (ii) the highest income of the poorest 1,000persons.

2019 back –QN-3b

incomes of a group of 1000persons were found to be normally distributed with mean Rs. 52,000 and standard deviation Rs. 6,000. Find

(i) The highest income of poorest 10% of the persons.

(ii)Lowest income of richest 20% of the persons.

2019 Back QN-6

Out of 9,000 families 4 children each, how,many families would you expect to have 3 boys and 1 girl, the birth of male child and female child is assumed equal.

2018 August Q.No. 3a – 4.5 Marks

In an examination, 10% of the students got less than 30marks and 95% of the students got less than 85 marks. Assuming the distribution to be normal, find the mean and standard deviation of the marks distribution.

2018 January Q.No. 3b-4.5 Marks

The marks obtained by 3000 students in an examination are normally distributed with mean 60 and standard deviation 10

(i)Find the lowest marks of top 25% of the students.

(ii)Find the limits of middle 60% of the students.

2017 Make up Q. No. 5b — 2015 Make. No. 3b- 9 Marks

Incomes of a group of 1000 persons were found to be normally distributed with mean Rs. 520 and standard deviation Rs. 60. Find:

i.The highest income of poorest 10% of the persons:

ii. Lowest income of richest 20% of the persons.

2015 QN 3b – 9Marks

The marks obtained by 5000 students in an examination are normally distributed with a mean of 65 and a standard deviation 20. Estimate (i) the lowest marks of the top 10% of students. (i) highest marks of poorest 500 students.

2018 June (Makeup) Q.No. 8

The life of a certain product is assumed to be normally distributed with mean 160 hours and standard deviation of 24 hours. What is the probability that the life of a randomly chosen product is (i) less than 122 hours (i) between 141 hours and 190 hours?

2016 Q.No. 7 – 3 marks

The weekly wages of 1000 workers are normally distributed with mean income of \$70 with a standard deviation of \$5. Estimate the number of workers whose weekly wages will be

(i) between \$69 and \$72 (i) less than \$63.

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