Determining Probability For a Normal Random Variable

To decrease the amount of time it takes to deliver packages, a delivery company purchased computer software that finds the optimal route for making deliveries based upon the input of the package destinations. In the past the average amount of time it took to complete deliveries was 9.4 hours with a standard deviation of 0.8 hours. Since purchasing the software the average delivery time over twenty delivery days was 8.6 hours. At the 0.05 level of significance, test whether the software package has reduced the average time it takes to complete deliveries.

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Let mu be the mean time that it takes to complete deliveries, we want to test ...

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The solution gives detailed steps on performing the hypothesis tesing assuming the data is normally distribution. Both population mean and standard deviation are given in the question.

Find the probability that a standard normalrandomvariable will assume a value between:
a. z = 1.5 and z = .75
b. Greater than 1.25
c. Find a z such that 70% of the area is above that value.

Please help me to answer the given problem in detail:
Let X be a normal distributed randomvariable with u=100 and o=10. The probability that X is between 70 and 100 is:
a. 8%
b. 84%
c. 95%
d. The answer not listed

The ages of 50 women are approximately normally distributed with a mean of 48 years and a standard deviation of 5 years. One women is randomly selected from the group, and her age is observed.
Find the probability that her age will fall between 56 and 59 years.
Find the probability that her age will exceed 41 years.

X~N(500,400) Determine the following
RandomVariable X
a) P( X <= 515 )
b) P( X <= 515 | X > 450 ) (note: "|" implies given)
c) P( 20 < X^(1/2) <= 25 ) ( i.e. 20 < "square root of X" < 25 )
please clearly state each step for each part. The attached file states the problem again.

Standard normal probabilities
Let Z be a standard normal random variable. Calculate the following probabilities using the calculator provided. Round your responses to at least three decimal places.
P (z > - 0.82) =
P (z ≤ 0.77) =
P( -0.81 < z < 1.25) =

Each item produced by a certain manufacturer is, independantly, of acceptable quality with probability 0.95. Approximate the probability that at most 10 of the next 150 items produced are unacceptable.

Cruise ships of the Royal Viking line report that 80 percent of their rooms are occupied during September. For a cruise ship having 800 rooms, what is the probability that 665 or more are occupied in September?

1. A box contains four tickets, one marked with a star and the other three blank. One draw is made from this box at random.
a. What does "at random" mean?
b. What is the randomvariable in this experiment?
c. Write the probability model corresponding to this randomvariable. Explain your answer. Also verify t

The following problem develop the concept of determining the probability distribution of a randomvariable and its mean and variance.
A fair coin is tossed three times. Describe the sample space Ω.
Let X be randomvariable that denotes the number of heads on the first toss. Describe the probability frequency
distribution of