Question

Study of sea turtles.research shows the shell Lengths have a distribution with a mean of 50cm and a standard dev of 10cm.in the study n76 turtles where captured the mean length for the sample was 55.5cm.how likely is it to observe a sample mean of 55.5cm or larger?

Answer 1

Answer on Question #63236 – Math – Statistics and Probability

Question

Study of sea turtles research shows the shell Lengths have a distribution with a mean of 50cm and a standard dev of 10cm. In the study n=76 turtles where captured the mean length for the sample was 55.5cm. How likely is it to observe a sample mean of 55.5cm or larger?

Solution

$$\begin{array}{l} P(\bar{X} > 55.5) = P\left(Z > \frac{55.5 - 50}{\frac{10}{\sqrt{76}}}\right) = P(Z > 4.794) = 1 - P(Z < 4.794) = \\ = 1 - 0.99999919 = 0.00000081, \text{ that is, } 0.000081\%. \end{array}$$

Thus, it is unlikely to observe a sample mean of 55.5cm or larger.

Answer: 0.000081 %.

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