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During one season of racing at the Talladega Superspeedway, the mean speed of the cars racing there was found to be 158.9 mph with a standard deviation of 10.0 mph. What speed represents the 33rd percentile for speeds of race cars at Talladega? Assume that the racing speeds are normally distributed.

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muhammadtalhashoaib

Answer:

154.5  mph

Explanation:

mean: 158.9 mph, SD: 10.0 mph

Need to convert the mean and SD into normal distribution.

We know P(X<z) = 0.33

From the normal distribution table,  P(X<z) = 0.33, z value is -0.44

P(X< -0.44) = 0.33

we know [tex]\frac{x-mean}{SD} = Z[/tex]

[tex]\frac{x-158.9}{10} = -0.44\\x=154.5[/tex]

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