Question

Ten percent of the population is left-handed. A class of 100 students is selected. Convert the binomial probability Plx<12) to a normal probability by using the correction for continuity. A P(x2 11.5) B. P(xs12.5) C. P(x>12.5) .d. P(x<11.5)

Answer 1

To convert the binomial probability P(x<=12) to a normal probability by using the correction for continuity, we can use the formula np = mean and npq = variance to find the mean and standard deviation of the normal distribution.

Step-by-step explanation:

To convert the binomial probability P(x<=12) to a normal probability by using the correction for continuity, we can use the formula np = mean and npq = variance to find the mean and standard deviation of the normal distribution. In this case, n = 100 and p = 0.1. Therefore, the mean (μ) is 10 and the standard deviation (σ) is sqrt(100*0.1*0.9) = 3. Therefore, to find P(x<=12) using the normal distribution, we need to calculate P(x<=12.5) because of the continuity correction. This can be calculated using the cumulative distribution function (CDF) of the standard normal distribution, which gives the probability that a standard normal variable is less than or equal to a certain value.

Using a standard normal distribution table or calculator, we can find that P(z<= (12.5-10)/3) = P(z<= 0.8333) = 0.7967. Therefore, P(x<=12) is approximately equal to P(x<=12.5), which is approximately 0.7967.