Suppose that a new treatment is successful in curing a common ailment 64% of the

Question

Suppose that a new treatment is successful in curing a common ailment 64% of the time. If the treatment is tried on a random sample of 85 patients, approximate the probability that at most 51 will be cured. Use the normal approximation to the binomial with a correction for continuity.

Round your answer to at least three decimal places. Do not round any intermediate steps.

Please provide only the correct answer and I will give you a good rate!

Question #9 / 20 Sir Francis Galton, in the late 1800s, was the first to introduce the statistical concepts of regression and correlation. He studied the relationships between pairs of variables such as the size of parents and the size of their offspring. Data similar to that which he studied are given below, with the variable x denoting the height (in centimeters) of a human father and the variable y denoting the height at maturity (in centimeters) of the father's oldest son. The data are given in tabular form and also displayed in the Figure 1 scatter plot. Also given are the products of the heights of fathers and heights of sons for each of the sixteen pairs. (These products, written in the column labelled "xy," may aid in calculations.) Height of father, Height of son, y xy (in centimeters) (in centimeters) 29326.5 26824.19 35815.56 31357.62 30635.48 39009.76 34577.38 171.5171.0 161.3 166.3 189.3 182.1 172.4 191.6 185.8 189.21 172.2 190- 203.6 186.1

Explanation / Answer

here mean =np=85*0.64=54.4

std deviation =(np(1-p))1/2 =4.425

hence probability that at most 51will be cured:

P(X<=51)=P(Z<(51.5-54.4)/4.425)=P(Z<-0.66)=0.255 ( please try 0.256 if this comes wrong due to rounding error and revert)

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