Question

suppose that 32% of all births in a certain region take place by caesarian section each year
a. in a random sample of 800 births, how many, on average, will take place by caesarian section?
b. what is the standard deviation of the number of caesarian section births in a sample of 800 births?
c. use your answers to parts a and b to form an interval that is likely to contain the number of caesarian section births
in a sample of 800 births
a. on average, 256 out of 800 births will take place by caesarian section
(round to the nearest whole number as needed.)
b. the standard deviation in a sample of 800 births is 13 19
(round to two decimal places as needed )
c. the number of caesarian section births is 95% likely to be in the interval (□□) using the empirical rule
(round to one decimal place as needed.)

Explanation:

Step1: Recall the empirical rule

The empirical rule states that for a normal distribution, approximately 95% of the data lies within \( \mu\pm2\sigma \), where \( \mu \) is the mean and \( \sigma \) is the standard deviation.

Step2: Identify the values of \( \mu \) and \( \sigma \)

From part (a), \( \mu = 256 \). From part (b), \( \sigma=13.19 \)

Step3: Calculate the lower and upper bounds of the interval

The lower bound \( L=\mu - 2\sigma \)

$$
LATEXBLOCK0
$$

The upper bound \( U=\mu + 2\sigma \)

$$
LATEXBLOCK1
$$

Answer:

The interval is \( (229.6,282.4) \)