please Help! Will give the most points and Branliest for detailed solving!
1. The heights of 18-year-old men are approximately normally distributed, with mean 68
inches and standard deviation 3 inches.
a. What is the probability that an 18-year-old man selected at random is between
67 and 69 inches tall?
b. If a random sample of ten 18-year-old men is selected, what is the probability
that the mean height of the sample is between 67 and 69 inches?
2. Let x be a random variable that represents level of glucose in the blood (mg per deciliter
of blood) a er a 12-hour fast. The glucose level is approximately normal with a mean of
85 and a standard deviation of 25.
a. What is the probability that a sample of 10 people have a mean glucose level less
than 84.5?
b. What is the probability that a sample of 100 people have a mean glucose level
less than 84.5?
3. Let x be a random variable that represents weights in kilograms of healthy adult female deer in December in Mesa Verde National Park. It has a distribution that is skewed to the right with a mean of 63.0 kg and standard deviation of 7.1 kg. What is the
probability that a random sample of 50 has a mean weight less than 64.2 kg?
4. The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.5 minutes and a standard deviation of 2.5 minutes. Assume that the distribution of taxi
and takeoff times is approximately normal. You may assume that the jets are lined up
on a runway so that one taxies and takes off immediately a er the other, and they take
off one at a time on a given runway. What is the probability that for 36 jets on a given
runway the average taxi and takeoff time will be less than 8.9 minutes?
5. The average fuel consumption for a Boeing 747 commercial jet in cruising position is
3213 gallons of jet fuel per hour. Assume that the fuel consumption distribution is
approximately normal with a standard deviation of 180 gallons of jet fuel per hour.
What is the probability that a sample of 20 jets used on average between 3000 and
3200 gallons per hour?
6. Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have
shown that the watches have an average life of 38 months before certain electronic
components deteriorate, causing the watch to become unreliable. The standard
deviation of watch lifetimes is 5 months. What is the probability that a sample of 50
watches only lasts an average of 37.4 months?
