Answer:
a. The value of alpha is 3.014 and the value of beta is 12.442
b. The probability that data transfer time exceeds 50ms is 0.238
c. The probability that data transfer time is between 50 and 75 ms is 0.176
Step-by-step explanation:
a. According to the given data we have that the mean and standard deviation of the random variable X are 37.5 ms and 21.6.
Therefore, E(X)=37.5 and V(X)=(21.6)∧2
To calculate alpha we would have to use the following formula:
alpha=E(X)∧2/V(X)
alpha=(37.5)∧2/21.6∧2
alpha=1,406.25
/466.56
alpha=3.014
To calculate beta we would have to use the following formula:
β= V(X)
∧2/E(X)
β=(21.6) ∧2/37.5
β=466.56
/37.5
β=12.442
b. E(X)=37.5 and V(X)=(21.6)∧2
Therefore, P(X>50)=1−P(X≤50)
Hence, To calculate the probability that data transfer time exceeds 50ms we use the following formula:
P(X>50)=1−P(X≤50)
=1−0.762
=0.238
The probability that data transfer time exceeds 50ms is 0.238
c. E(X)=37.5 and V(X)=(21.6)∧2
Therefore, P(50<X<75)=P(X<75)−P(X<50)
Hence, To calculate the probability that data transfer time is between 50 and 75 ms we use the following formula:
P(50<X<75)=P(X<75)−P(X<50)
=0.938−0.762
=0.176
The probability that data transfer time is between 50 and 75 ms is 0.176
