Answer:
The probability he throws it between 50 feet and 60 feet is 0.48
Step-by-step explanation:
* Lets revise how to find the z-score
- The rule the z-score is z = (x - μ)/σ , where
# x is the score
# μ is the mean
# σ is the standard deviation
* Lets solve the problem
- The mean is 50 feet
- The standard deviation 5 feet
- We need to find the probability of his throws between 50 feet and
60 feet
∵ z = (x - μ)/σ
∵ x = 50 and 60
∵ μ = 50
∵ σ = 5
- Substitute these values in the rule above
∴ z =
∴ z = 0
∴ z =
∴ z = 2
- Lets use the normal distribution table of z to find the corresponding
area to z score
∵ P(z > 0) = 0.5
∵ P(z < 2) = 0.97725
- Subtract the two areas
∴ P(0 < z < 2) = 0.97725 - 0.5 = 0.47725
∵ P(50 < x < 60) = P(0 < z < 2)
∴ P(50 < x < 60) = 0.47725
∴ P(50 < x < 60) ≅ 0.48
<em>The probability he throws it between 50 feet and 60 feet is 0.48</em>