Answer:
Step-by-step explanation:
Binomial distribution can be used in this case
P(x=r) nCr×q^n-r×q^r
n =15
p = 75/100= 0.75
q= 1-p = 0.25
a) The distribution of x is discrete
b) the probability that x is at least 10
= probability of x greater than or equal to 10 = P(x= 10) +P(x = 11) + P(x=13) +P(x=14) +P(x =15)
P(x= 10) =15C10×0.25^5×0.75^10=0.1651
P(x = 11) =15C11×0.25^4×0.75^11=0.2252
(x=12) =15C1×0.25^3×0.75^12=0.2251
(x=13) =15C13×0.25^2×0.75^13=0.1559
(x=14)=15C14×0.25^1×0.75^14=0.0668 (x=15)=15C15×0.25^0×0.75^15=0.0134
probability of x greater than or equal to 10 = P(x= 10) +P(x = 11) + P(x=13) +P(x=14) +P(x =15)= 0.1651+ 0.2252+0.2251+0.1559+0.0668+0.0134
= 0.8381
c)
The probability that X is at most 10 =
1-probability of x is greater than or equal to 11
= 1- (0.2252+0.2251+0.1559+0.0668+0.0134 =1-0.673
=0.327
d)P(x=10)=0.1651
Mean = np =15*0.75=15
Standard deviation = npq=15×0.25=2.8125
Variance =2.8125^2=7.91