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Answer:
a. Mean: 9.5.
Standard deviation: 2.18.
b. The critical value for signficantly low girl births is 5.14.
The critical value for signficantly high girl births is 13.86.
Step-by-step explanation:
a) If we take a sample of 19 births, all with individual probability of 0.5, we have a random binomial variable with n=19 and p=0.5.
This random variable will have mean and standard deviation calculated as:
b) Range rule of thumb: The standard deviation is approximately a quarter of the range, difference between the maximum and minimum value.
The range rule of thumb tells us that the expected minimum and maximum value are 2 standards deviation below or above, respectively, from the mean.
Then, the extreme expected values are:
The critical value for signficantly low girl births is 5.14.
The critical value for signficantly high girl births is 13.86.