Answer: P(x ≥ 47) = 0.25
Step-by-step explanation:
Since the distribution of the life expectancies of a certain protozoan is normal, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = life expectancies of the certain protozoan.
µ = mean
σ = standard deviation
n = number of samples
From the information given,
µ = 46 days
σ = 10.5 days
n = 49
The probability that a simple random sample of 49 protozoa will have a mean life expectancy of 47 or more days is expressed as
P(x ≥ 47) = 1 - P(x < 47)
For x = 47
z = (47 - 46)/(10.5/√49) = 0.67
Looking at the normal distribution table, the probability corresponding to the z score is 0.0.75
P(x ≥ 47) = 1 - 0.75 = 0.25
