 # Statistics Questions on Normal Distribution

1.
Find the probability for the standard normal random variable z

P(-3.08=z=3.08)

2.
Find the area under the standard normal probability distribution between the following pairs of Z-scores
z=0 and z=2.00
z=0 and z=1.00
z=0 and z=3.00
z=0 and z=0.74

3.
Suppose x is a normally distributed random variable with u=11 and s =2
Find each of the following probabilities
P(X =15)=
P(X = 9.5)=
P(11.78 = x = 15.84)=
P(5.72 = x = 13.84)=

4.
The age of a group of 50 women are approximately normally distributed with a mean of 29 years and a standard deviation of 6 years. One woman is randomly selected from the group and her age is observed.
Find the probability that her age will fall between 54 and 61 years__
Find the probability that her age will fall between 48 and 53 years__
Find the probability that her age will be less than 35 years__
Find the probability that her age will exceed 40 years_____
(round to four decimal places as needed)

5.
The mean gas mileage for a hybrid car is 57 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed of 3.5 miles per gallon.
What is the probability that a randomly selected hybrid gets more than 60 miles per gallon?
What is the probability that a randomly selected hybrid gets 53 gallon or less?
What is the probability that a randomly selected hybrid gets 58 and 62 per gallon?
What is the probability that a randomly selected hybrid gets less than 45 gallon?
6.
Resource reservation protocol was originally designed to establish singling links for stationary networks. RSVP was applied to mobile wireless technology. A simulation study reveals that the transmission delay (measured in milliseconds) of a rsvp link wireless device has an approximate normal distribution with mean u=49.5 milliseconds and s-8.5 milliseconds.
What the probability that the transmission delay is less than 57 milliseconds?
P(x<57)=___

Solutions are type written and provide step by step answers on how to get to the final results!

Subjects: Statistics
Topic: Normal Distribution
Level: College
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### Statistics Homework Solutions

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Subjects: Statistics
Topic: Normal Distribution
Level: College
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## Statistics Homework Solutions

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