Answer:
The probability that a simple random sample of 64 protozoa will have a mean life expectancy of 54 or more days is P(M>54)=0.00004.
Step-by-step explanation:
In this case, we have a population lifetime normally distributed with mean 49 and standard deviation 10.2.
We take a sample of size n=64.
Then, we can calculate the z-score for a sample mean M=54, in order to calculate P(M>54):
[tex]z=\dfrac{X-\mu}{\sigma/\sqrt{n}}=\dfrac{54-49}{10.2/\sqrt{64}}=\dfrac{5}{1.275}=3.922\\\\\\P(M>54)=P(z>3.922)=0.00004[/tex]
The probability that a simple random sample of 64 protozoa will have a mean life expectancy of 54 or more days is P(M>54)=0.00004.
