The average scuba diver can stay under water for 42 minutes with a standard deviation of 8 minutes.(show graph)
B. what is the probabilty that a diver stays under for the less than 53 minutes?
c.what is the probabilty that a diver stays under between 25 and 50?
d. what is the probabilty that a diver stays under for more than 52 mintues?
e.find the cutoff number for the middle 50% of the time a diver stays down?
f.find the top 15% of time the diver stays down?
g. find the bottom 20%of the time a diver stays down?
To answer these questions, we can use the concept of the normal distribution.
A. The graph of the normal distribution for this scenario would show a bell-shaped curve, with the x-axis representing the time underwater and the y-axis representing the probability. The mean of the distribution would be 42 minutes and the standard deviation would be 8 minutes. The graph would be symmetrical around the mean, with the highest point of the curve at the mean.
B. To find the probability that a diver stays under water for less than 53 minutes, we need to calculate the area under the curve to the left of 53 minutes. We can use the Z-score formula to find the Z-score corresponding to 53 minutes, and then use a Z-table or a calculator to find the corresponding probability.
C. To find the probability that a diver stays under water between 25 and 50 minutes, we need to calculate the area under the curve between 25 and 50 minutes. We can again use the Z-score formula to find the Z-scores corresponding to 25 and 50 minutes, and then find the difference between the probabilities associated with those Z-scores.
D. To find the probability that a diver stays under water for more than 52 minutes, we need to calculate the area under the curve to the right of 52 minutes. We can again use the Z-score formula to find the Z-score corresponding to 52 minutes and then find the complement of the probability associated with that Z-score.
E. To find the cutoff number for the middle 50% of the time a diver stays down, we need to find the Z-scores corresponding to the percentiles of 25% and 75%. These Z-scores would give us the corresponding times underwater.
F. To find the top 15% of the time the diver stays down, we need to find the Z-score corresponding to the 85th percentile and then find the corresponding time underwater.
G. To find the bottom 20% of the time a diver stays down, we need to find the Z-score corresponding to the 20th percentile and then find the corresponding time underwater.
Note: The specific calculations and values would depend on the standard normal distribution table or a statistical calculator.