Answer:
The probability is 0.20
Step-by-step explanation:
a) 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
- Bob's golf score at his local course follows the normal distribution
- The mean is 92.1
- The standard deviation is 3.8
- The score on his next round of golf will be between 82 and 89
- Lets find the z-score for each case
# First case
∵ z = (x - μ)/σ
∵ x = 82
∵ μ = 92.1
∵ σ = 3.8
∴ [tex]z=\frac{82-92.1}{3.8}=\frac{-10.1}{3.8}=-2.66[/tex]
# Second case
∵ z = (x - μ)/σ
∵ x = 89
∵ μ = 92.1
∵ σ = 3.8
∴ [tex]z=\frac{89-92.1}{3.8}=\frac{-3.1}{3.8}=-0.82[/tex]
- To find the probability that the score on his next round of golf will
be between 82 and 89 use the table of the normal distribution
∵ P(82 < X < 89) = P(-2.66 < z < -0.82)
∵ A z-score of -2.66 the value is 0.00391
∵ A z-score of -0.82 the value is 0.20611
∴ P(-2.66 < z < -0.82) = 0.20611 - 0.00391 = 0.2022
* The probability is 0.20
