One year, demand for sperm whale oil was particularly high and Captain Ahab decided to hunt onlythose whales. The length of a sperm whale in the 1840s was normally distributed with mean 16.1meters and standard deviation 1.5 meters.(a) What is the probability that the first four whales they catch are all longer than 16.4meters?(b) If the selection and capture of the whales is random, what is the probability that themean length of the first 25 whales they capture is at least 16.3 meters.(c) Upon return to Nantucket, Captain Ahab reports how many whales they caught, andthat the mean length of sperm whales they caught was 16.3 meters. His colleague Captain Bildadexclaims, “But there’s less than a 1% chance of getting a mean that high or higher if the truepopulation mean and standard deviation are what we think they are!”Approximately how many whales did Ahab tell Bildad they caught?(d) The next year, they catch 123 whales with a mean length of 16.4 meters, and astandard deviation of 1.4 meters. Based in this sample, find a 95%-confidence interval for the truepopulation mean length of sperm whales
One year, demand for sperm whale oil was particularly high and Captain Ahab decided to hunt only
those whales. The length of a sperm whale in the 1840s was
meters and standard deviation 1.5 meters.
(a) What is the
meters?
(b) If the selection and capture of the whales is random, what is the probability that the
mean length of the first 25 whales they capture is at least 16.3 meters.
(c) Upon return to Nantucket, Captain Ahab reports how many whales they caught, and
that the mean length of sperm whales they caught was 16.3 meters. His colleague Captain Bildad
exclaims, “But there’s less than a 1% chance of getting a mean that high or higher if the true
population mean and standard deviation are what we think they are!”
Approximately how many whales did Ahab tell Bildad they caught?
(d) The next year, they catch 123 whales with a mean length of 16.4 meters, and a
standard deviation of 1.4 meters. Based in this sample, find a 95%-confidence interval for the true
population mean length of sperm whales
"Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved."
(a)
The probability that the first four whales they catch are all longer than 16.4 meters is,
Thus, the probability that the first four whales they catch are all longer than 16.4 meters is 0.3446.
(b)
The probability that the mean length of first 25 whales they capture is at least 16.3 meters is,
Thus, the probability that the mean length of first 25 whales they capture is at least 16.3 meters is 0.2524.
Step by step
Solved in 3 steps with 3 images
