Sixty two percent of data scientists prefer R to Python for predictive modeling.

Question

Sixty two percent of data scientists prefer R to Python for predictive modeling. If a sample of 500 data scientists are selected, find the probability that at least 290 prefer R to Python.

Determine p and n

Find the mean, µ

Find 2 and

Write the probability formula.

Rewrite the formula using the continuity correction factor:

Look up the z-value in the z-table and nd the probability we are looking for.

Find 2 and

Write the probability formula.

Rewrite the formula using the continuity correction factor:

Look up the z-value in the z-table and nd the probability we are looking for.

Explanation / Answer

p = 0.62, n = 500
Normal Approximation to Binomial Distribution
Mean ( np ) =500 * 0.62 = 310
Standard Deviation ( npq )= 500*0.62*0.38 = 10.8536
Normal Distribution = Z= X- u / sd                   
P(X > 290) = (290-310)/10.8536
= -20/10.8536 = -1.8427
= P ( Z >-1.843) From Standard Normal Table
= 0.9673

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