Problems on Normal Distribution:
1. The mean and standard deviation of the marks obtained by 1000 students
in an examination are respectively 34.5 and 16.5. Assuming the normal
distribution, find the approximate number of students expected to obtain
marks between 30 and 60.
2. If 𝑧 is a normal variate, find the area under the normal curve
(a) to the left of 𝑧 = −1.78
(b) to the right of 𝑧 = −1.45
(c) corresponding to −0.8 ≤ 𝑧 ≤ 1.53
(d) to the left of 𝑧 = 2.52 and to the right of 𝑧 = 1.83
3. A manufacturer knows from experience that the resistance of resistors he
produces is normal with mean 100 Ohms and standard deviation is 2
Ohms. What percentage of resistors will have resistance between98 Ohms
and 102 Ohms.
4. Find the mean and standard of a normal distribution in which 7% of items
are under 35 and 89% are under 63.