Probability of a seal living less than 7.4 years, P(X < 7.4) = 0.023
Explanations:The distribution is said to be a normal distributuion.
For a normal distribution, you first calculate the z value.
[tex]\begin{gathered} \text{Average life, }\mu\text{ = 13.8} \\ \text{Standard Deviation, }\sigma\text{ = 3.2} \\ \text{The observed value, x = 7.4} \end{gathered}[/tex]The z value is calculated as:
[tex]\begin{gathered} \text{z = }\frac{\text{x -}\mu}{\sigma} \\ z\text{ = }\frac{7.4-13.8}{3.2} \\ z\text{ = }\frac{-6.4}{3.2} \\ z\text{ = -2} \end{gathered}[/tex]The probability of a seal living less than 7.4 years can be represented mathematically as:
P ( X < 7.4) Which can be interpreted as P(z < -2)
Checking this is in standard normal table:
P( z < -2) = 0.02275
Approximating to 3 decimal places, P(z < -2) = 0.023
Therefore, P ( X < 7.4) = 0.023
