According to previous studies, 12% of the United States population is left-handed. Not knowing this, a high school student claims that the percentage of left-handed people in the US is 14%.

The student is going to take a random sample of 1650 people in the US to try to gather evidence to support the claim. Let p be the proportion of left-handed people in the sample.

a). Find the mean of p.

b). Find the standard deviation of p.

c). Compute an approximation for

P (p < 0.14), which is the probability that there will be 14% or few left-handed people in the sample.

Round your answer to at least 4 decimal places.