Elementary Statistics and Computer Application

Application

Application

1. Quality control measures and sampling process in industries to classify items as defectives or non-defective.
2. Medical applications such as success or failure, cure or no-cure.
Example 1

• Eight coins are tossed simultaneously. Find the probability of getting atleast six heads.
Solution:

• Here number of trials, n = 8, p denotes the probability of getting a head


• If the random variable X denotes the number of heads, then the probability of a success in n trials is given by
• P(X = x) = ncx p^x q^n-x , x = 0 , 1, 2, ..., n



• Probability of getting atleast six heads is given by




Example 2
Ten coins are tossed simultaneously. Find the probability of getting

• Atleast seven heads
• Exactly seven heads
• Atmost seven heads
Solution





The probability of getting x heads throwing 10 coins simultaneously is given by
P(X = x) = nC_x p^x q^n-x. , x = 0 , 1, 2 , ..., n


i) Probability of getting atleast seven heads
P(x >7) = P (x = 7) + P(x = 8) + P (x = 9) + P (x =10)



ii) Probability of getting exactly 7 heads

iii) Probability of getting almost 7 heads
P( x < 7) = 1 – P(x > 7)
= 1 symbol{ P(x = 8) + P (x = 9) + P(x = 10)}