Question

Assume 46 percent of data scientists prefer R to Python for predictive modeling. If a sample of 450 data scientists are selected, find the probability that at least 200 prefer R to Python by the following steps:

Step 1 Determine p and n:

Step 2 Find the mean, µ.

Step 3 Find σ² and σ.

Step 4 Write the binomial probability statement we are evaluating.

Step 5 Rewrite the statement from Step 4 using the continuity correction factor.

Step 6 Describe the distribution we are using to calculate our probability. Why are we able to use this distribution?

Step 7 Find the z-score for Step 5.

Step 8 Using the appropriate z-value, find the probability we are looking for.

Answer 1

Step 1:

Here p = 0.46, n = 450

Step 2: Mean :

µ = np= 450 * 0.46 = 207

Step 3:

² = n*p* ( 1 -P ) = 450* 0.46 * ( 1 - 0.46 ) = 111.78

Step 4: Here we need to find

p ( x 200 )

Step : The continuity correction is

p ( x 199.5 )

Step 6: Here we have n is very large, so we use normal approximation to Binomial distribution.

Here np = 207 > 10 and nq = 450 * 0.54 = 243

Step 7 :

p ( x 199.5 )

= p ( z -0.71 )

Step 8:

p ( z -0.71 )

= 1 - p ( z < -0.71 )

= 1 - 0.2389

= 0.7611