Chapter 6: Q. 6.9 (page 376)

The golf scores for a school team were normally distributed with a mean of $68$ and a standard deviation of three.
Find the probability that a golfer scored between $66$ and $70$

Short Answer

Expert verified

The probability that a golfer scored between $66$ and $70$ is $0.4972$ .

Step by step solution

Given Information

Given in the question that, the golf scores for a school team were normally distributed with a mean of $68$ and a standard deviation of three.

We have to find the probability that a golfer scored between $66$ and $70$ .

Explanation

From the information we obtain that any golf scores were normally distributed. So that $X ~ N (68, 3)$

Therefore, we can compute the required probability as follow:

$P (66 < x < 70) = P (x < 70) - P (x < 66)$

$= P (\frac{x - μ}{σ} < \frac{70 - μ}{σ}) - P (\frac{x - μ}{σ} < \frac{66 - μ}{σ})$

$= P (Z < \frac{70 - 68}{3}) - P (Z < \frac{66 - 68}{3})$

$= P (Z < 0.67) - P (Z < - 0.67)$

$= 0.7486 - 0.2514 \{\begin{array}{l} From standard \\ normal table \end{array}\}$

localid="1648196054872" $= 0.4972$

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The golf scores for a school team were normally distributed with a mean of $68$ and a standard deviation of three.
Find the probability that a golfer scored between $66$ and $70$

Short Answer

Step by step solution

Given Information

Explanation

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The golf scores for a school team were normally distributed with a mean of 68and a standard deviation of three.Find the probability that a golfer scored between 66and70

Short Answer

Step by step solution

Given Information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Discrete Mathematics

Mechanics Maths

Decision Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

The golf scores for a school team were normally distributed with a mean of $68$ and a standard deviation of three.
Find the probability that a golfer scored between $66$ and $70$