Final answer:
To answer the questions, analyze the data collected from 23 flights. Calculate probabilities of O-ring failure based on different temperature conditions and determine if O-ring failure is independent of temperature. Given O-ring failure at temperatures greater than 65°F, it is recommended to reconsider the Challenger launch.
Step-by-step explanation:
To answer the given questions, we need to analyze the data collected from 23 flights. Based on the data, we can calculate the probability of at least one O-ring failing, regardless of temperature, by finding the number of flights with at least one O-ring failure and dividing it by the total number of flights.
For the second question, we need to find the number of flights with O-ring failure and a temperature of 65°F or lower, and divide it by the total number of flights with a temperature of 65°F or lower. For the third question, we need to find the number of flights with O-ring failure and a temperature greater than 65°F, and divide it by the total number of flights with a temperature greater than 65°F.
To determine if O-ring failure is independent of the temperature being 65°F or lower, we need to compare the conditional probabilities of O-ring failure given a temperature of 65°F or lower and O-ring failure regardless of temperature.
If the conditional probabilities are the same, then O-ring failure is independent of the temperature. Finally, the recommendation regarding the ill-fated Challenger launch would depend on various factors, including the probability of O-ring failure and the risks associated with it. Considering that O-ring failure occurred even at temperatures greater than 65°F, it would be prudent to reconsider the launch.