Question - Marketing and Consumer Behavior More children are being rushed to the hospital because they were able to push down and twist the cap on a medication bottle and were poisoned by a common drug. A recent research study suggested that 25% of all preschool children can open a medication bottle and 10 preschool children are selected at random. Let the random variable X be the number of children who can open the bottle.
a. Construct a probability histogram for the random variable X.
b. Find the mean, variance, and standard deviation of X. Indicate the mean on the graph from part (a).
c. Find P(μ - σ ≤ X ≤ μ + σ) and indicate this probability on the graph from part (a).
d. Suppose these 10 children try to open a medicine bottle with a new design for the cap and one child is able to open the bottle. Is there any evidence to suggest that the new cap is more effective in stopping children from opening the bottle? Justify your answer.