Question 7:
The probability of a customer making a purchase is 0.45 (or 45%).
We can use the binomial probability formula to find the probability that 2 of the next 3 customers will make a purchase. The formula is:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
X = the number of successful outcomes (purchases)
k = 2 (the number of successful outcomes we want)
n = 3 (the number of trials)
p = 0.45 (the probability of a successful outcome)
So,
P(X = 2) = (3 choose 2) * (0.45)^2 * (1-0.45)^(3-2)
P(X = 2) = 3 * (0.45)^2 * (0.55)^1
P(X = 2) = 0.4035 or 40.35%
So, the probability that 2 of the next 3 customers will make a purchase is 40.35%.
Question 8:
Since we know the average age of vehicles registered in Ethiopia is 12 years and the standard deviation is 9 years, we can assume that the age of vehicles follows a normal distribution.
To find the probability that the mean of the ages of 32 vehicles sampled is between 8 and 15 years, we need to use the Z-score formula, which is:
Z = (X - μ) / σ
Where:
X = the mean age of the sample
μ = the population mean (12 years)
σ = the population standard deviation (9 years)
We can find the Z-score for 8 years by putting 8 in place of X:
Z = (8 - 12) / 9 = -4/3
and the Z-score for 15 years:
Z = (15 - 12) / 9 = 1/3
Now we can find the probability that the mean age of the sample is between 8 and 15 years by finding the area under the normal distribution curve between these two Z-scores.
We can use the standard normal table to find the probability between -4/3 and 1/3.
The probability is between 0.3256 and 0.3604, which is a small probability. It means that it is rare to have the mean of the age of 32 vehicles sampled between 8 and 15 years.