When Noah goes bowling, his scores are normally distributed with a mean of 150 and a standard deviation of 12. What is the probability that the next game Noah bowls, his score will be between 135 and 167, to the nearest thousandth?

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absor201 absor201 · Answer 1 · 2020-11-18T17:57:24+01:00

Answer:

The probability of his score being between 135 and 167 is 0.8151 or (0.8151*100=81.51%)

Step-by-step explanation:

Given that:

Mean = μ = 150

SD = σ = 12

Let x1 be the first data point and x2 the second data point

We have to find the z-scores for both data points

x1 = 135

x2 = 167

So,

[tex]z_1 = \frac{x_1-mean}{SD}\\= \frac{135-150}{12}\\=\frac{-15}{12}\\=-1.25[/tex]

And

[tex]z_2 = \frac{x_2-mean}{SD}\\z_2 =\frac{167-150}{12}\\=\frac{17}{12}\\= {1.416}[/tex]

We have to find area to the left of both points then their difference to find the probability.

So,

Area to the left of z1 = 0.1056

Area to the left of z2 = 0.9207

Probability to score between 135 and 167 = z2-z1 = 0.9027-0.1056 = 0.8151

Hence,

The probability of his score being between 135 and 167 is 0.8151 or (0.8151*100=81.51%)