Assianment ouestions
Answer each question completely and send your work back to your instructor, show all work. Jubily your answers clearty and completely with formulas and numerical solutions. shewing your work will allow your instructor to give you partial credit if you make a mistake but show that you still understand the problem.
1. In a survey, 600 mothers and fathers were suted steout the impertance of soorts for boys and glifs. Of the parents intervewed, 704 sald the genders are equal and should have equal epportunities to participate in sports.
A. What are the mean, standard deviation, and shape of the distribution of the sample propertion \( \beta \) of parents who say the genders are equal and should have equal opportunities? Be sure to justify your answer for the shape of the distribution. Use \( \pi=600 \). ( 1 point)
B. Using the normal approximation without the continuity correction, sketch the probability distribution curve for the distribution of \( \beta \). Shade equal areas on both sides of the mean to show an area that represents a probability of .95, and label the upper and lower bounds of the shaded area as values of \( p \)-hat (not \( x \)-scores). Show your calculations for the upper and (pwer bounds. (2)
Ao points)
C. Considering the sketch in part B, the shaded area shows a . 95 probability of what happening? In other words, what does the probability of -95 represent? (2) Using the normal approximation, what's the probability a randomly drawn sample of parents of size 600 will have a sample proportion between \( 67 \% \) and \( 73 \% \) ? Draw a sketch of the probability curve, shade the area representing the probability you're finding, and iabel the \( x \)-scores that represent the upper and lower bounds of the probablity you're finding. Don't use the continuity,
Now, use the exact binomial calculation to find the probability of getting between, but not including, \( 67 \% \) and \( 73 \% \) of the respondents in a sample of 600 who say the genders are equal and should have equal opportunities. To use the exact binomial, you'll need to convert the proportions to counts by multiplying each proportion by 600 . ( 1 point)
Now try it again, but this time find the probability of getting at least \( 67 \% \) but no more than \( 73 \% \). Use the exact binomial calculation. (1 point)
