The number of passengers on the Carnival Sensation during one-week cruises in the Caribbean follows the normal distribution. The mean number of passengers per cruise is 1,820 and the standard deviation is 120.

1. What percent of the cruises will have between 1,820 and 1,970 passengers?
2. What percent of the cruises will have 1,970 passengers or more?
3. What percent of the cruises will have 1,600 or fewer passengers?
4. How many passengers are on the cruises with the fewest 25 percent of passengers?

60. In establishing warranties on HDTV sets, the manufacturer wants to set the limits so that few will need repair at manufacturer expense. On the other hand, the warranty period must be long enough to make the purchase attractive to the buyer. For a new HDTV the mean number of months until repairs are needed is 36.84 with a standard deviation of 3.34 months. Where should the warranty limits be set so so that only 10 percent of the HDTVs need repairs at the manufacturer's expense?

The solution gives the details of computing probability based on normal distribution. Step by step procedure is given with interpretations of the results obtained.

Can you show work on the last set of problems I attempted to do the first two problems however, I don't know if that is right.
Thanks
2. Assume the standard normaldistribution. Fill in the blanks
(a) P( z < 2.00 ) = .9773
(b) P( z < -1.24 ) = .1075
(c) P( z > ) = .0793
(d) P( z > ) =

Find the indicated probabilities.
a. P (z > -0.89)
b. P (0.45 < z < 2.15)
Write the binomial probability as a normal probability using the continuity correction.
Binomial Probability Normal Probability
c. P ( x ≤ 56) P ( x < ? )
d. P ( x = 69 ) P ( ? < x < ?

I was wondering if someone could help explain the NormalDistribution to me, maybe in more simple terms. An example would also be useful. I am using the program Minitab to generate my answers to questions.

If x is normally distrubed with u = 20.0 and o = 4.0, determine the following:
a. P(x > 20.0)
b. P(16.0 < x < 24.0)
c. P(X < 12)
d. P(x = 22.0)
e. P(12.0 , x , 28.0)
f. P(x 15)

We are using a chart on standard normal (z) distribution: cumulative area from the LEFT showing Negative x Scores on one side and Positive (z) scores on the other.
a. P(z>2.61).
b. P(-1.62 < z < 2.81).
c. The z-score that would create a right tail of 31%.
d. The z-score that would create a left tail of 6.5%.

What are the characteristics of a standard normaldistribution? Can two distributions with the same mean and different standard distributions be considered normal? How might you determine if a distribution is normal from its graphical representation?