Answer:
The probability that the mean lifespan from the sample of 9 houseflies is less than 24 days is 30.85%
Step-by-step explanation:
Given that:
number of samples (n) = 9 houseflies,
Mean (μ) = 26 days,
Standard deviation (σ) = 12 days.
The Z score is used in statistics to know by how much a value is above or below the mean. The Z score (z) is given by the equation:
[tex]z= \frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
To get the probability that the mean lifespan from the sample of 9 houseflies is less than 24 days (i.e x = 24)
[tex]z= \frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }=\frac{24-26}{\frac{12}{\sqrt{9} } } = -0.5[/tex]
From the z table:
P(x < 24) = P(z < -0.5) = 0.3085 = 30.85%
Therefore, the probability that the mean lifespan from the sample of 9 houseflies is less than 24 days is 30.85%
