Statistical Methods for Science - Assignment 2

Statistical Methods for Science
Assignment 2
STUDENT NAME/ID
[Pick the date]

Question 1
(a) Probability that drug cause side effect to patient p =3/100 = 0.03
Total patient n = 5
Here, the distribution would be binomial distribution.
X ( 5 , 0.03 )
¿
P ( X=x ) =(5
x )(0.03x)¿ where , X =0 ,1 , 2 ,3 ... ..... 5
(b) Probability that none of the five patients experience side effects
Here, x=0
P ( X=0 )= (5
0 )(0.030)¿
Now,
Probability that at least two patients experience side effects
Here, x ≥ 2
P ( X ≥2 )=1−P ( x< 2 )
¿ 1− ( P ( x=0 ) + P ( x=1 ) )
¿ 1−{(5
0)(0.030 )¿
¿ 1− ( 0.8585+0.1328 )
¿ 0.0085
(c) Total patient n = 5

Here, the distribution would be Poisson distribution.
ƛ =np = 5(0.03) = 0.15
X ( 5 , 0.03 )
¿
P ( X=x ) =e−0.15 (0.15)x
x !
where , X =0 ,1 , 2 ,3 ... .... .
(c) Probability that none of the five patients experience side effects
Here, x=0
P ( X=0 ) = e−0.15 (0.15)0
0 ! =0.8607
Now,
Probability that at least two patients experience side effects
Here, x ≥ 2
P ( X ≥2 ) =1−P ( x< 2 )
¿ 1− ( P ( x=0 ) + P ( x=1 ) )
¿ 1− { e−0.15 ( 0.15 )0
0! + e−0.15 ( 0.15 )1
1! }
¿ 1− ( 0.8607+0.1291 )
¿ 0.0102
(d) It can be said that probabilities computed with the help of binomial distribution is lesser than
Poisson distribution. Further, the probabilities found in part (b) are more accurate than
computed in part (c).

Question 2
Mean μ=65
Standard deviation σ =5
Normal distribution
(a) % of eggs have weight above 70 grams P(X>70)
z= 70−65
5 =1
z=1
P ( X >70 ) =P ( Z >1 ) =0.1562(¿ standard normal table )
Hence, 15.92% of eggs have weight above 70 grams.
(b) % of eggs have scores between 70 and 75 grams
P ( 70< X <75 ) =P ( 70−65
5 < Z < 75−65
5 )
P ( 70< X <75 ) =P ( 1< Z <2 ) =0.977−84.13
P ( 70< X <75 )=0.1359(¿ standard normal table )
Hence, 13.59% of eggs have scores between 70 and 75 grams.
(c) Lowest weight of heaviest 5% egg
The p value = 1- 0.05 = 0.95
Z score for P (0.95) =1.645