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Statistical Analysis: Probability

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1.
Find the percentage of the total area under the standard normal curve between the given z-scores.
a) Z=.64 and z =2.11
b) Z= -1.63 and z = -1.08
c) Z= - 2.91 and z = -.51

2.
Find a z -score satisfying each of the given conditions
a) 1% of the total area is to the left Z
b) 25% of the total area is to the right of Z

Assume that the following distributions are all normal 2-5
1.
According to the label, a regular can of soup holds an average of 305 grams, with a standard deviation of 4.2 grams. What is the probability that a can will be sold that holds more than 306 grams
2.
A general Electric soft white three -way light bulb has an average life of 1200 hours , with a standard deviation of 50 hours .Find the probability that the life of one of these bulbs will be between 1150 and 1300hours
3.
The scores on a standardized test in a suburban high school have a mean of 80 ,with a standard deviation of 12 .What is the probability that a student will have a score less than 60
4.
The production of cars per day at an assembly plant has mean 120.5 and standard deviation 6.2.Find the probability that fewer than 100 cars are produces on a random day.
5.
The driving distance to work for residents of a certain community has mean 21 and standard deviation 3.6 miles. What is the probability that an individual drives between 10 and 20 miles to work
6.
For certain bird species, with appropriate assumptions, the number of nests escaping predation has a binomial distribution. Suppose the probability of success (that is a nests escaping predation) is 3. Find the probability that at least half of 26 nests escape predation.
7.
In 2007 -2008, 66%of all undergraduates received some type of financial aid. Suppose 50 under graduates are selected at random.
A) Find the probability that at least 35 received financial aid
B) Find the probability that at most 25 received financial aid
8.
In 2007 -2008, 34% of all undergraduates took out a federal Stafford loan. If a random sample of 250 students is selected, find the probability that at most 75 students took out a federal Stafford
9.
The probability that a male will be color blind is 0.42 .Find the probabilities that, in a group of 53 men, the given conditions will be true
a) Exactly 6 are color blind
b) No more than 6 are color blind
c) At least 1 is color blind

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Solution Preview

1.
Find the percentage of the total area under the standard normal curve between the given z-scores.

a) Z=.64 and z =2.11
P(0.64<z<2.11)=P(z<2.11)-P(z<0.64)=0.9826-0.7389=0.2437=24.37%
b) Z= -1.63 and z = -1.08
P(-1.63<z<-1.08)=P(z<-1.08)-P(z<-1.63)=0.1401-0.0516=0.0885=8.85%
c) Z= - 2.91 and z = -.51
P(-2.91<z<-0.51)=P(z<-0.51)-P(z<-2.91)=0.3050-0.0018=0.3032=30.32%

2.
Find a z -score satisfying each of the given conditions
a) 1% of the total area is to the left Z
P value is 0.01, the corresponding z is -2.33.
b) 25% of the total area is to the right of Z
P value is 1-0.25=0.75, the corresponding z is 0.67

Assume that the following distributions are all normal 2-5
1.
According to the label, a regular can of soup holds an average of 305 grams, with a standard deviation of 4.2 grams. What is the probability that a can will be sold that holds more than 306 ...

Solution Summary

The expert finds the percentage of the total area under the standard normal curves between the given z-scores. Conditions to find z-scores are satisfied.

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Continuous Probability Distribution - Statistical Analysis

JENN Inc. supplies under-hood emission control air pumps to the automotive industry. The pump is vacuum-powered and works while the engine is operating., cleaning the exhaust by pumping extra oxygen into the exhaust system. If a pump fails before the vehicle in which it is installed has travelled 50,000 miles, Federal emission regulations require that it be replaced at no cost to the vehicle owner. The company's current air pump lasts an average of 61,000 miles, with a standard deviation of 9,000 miles. The number of miles a pump operates before becoming ineffective has been found to follow a Normal distribution.

1. For the current pump design, what percentage of the company's pumps will have to be replaced at no charge to the vehicle owner? (show analysis for practice prob and show why)

2. What percentage of the company's pumps will fail at exactly 50,000 miles? (show analysis and why)

3. What percentage of the company's pumps will fail at mileage between 42,000 and 57,000 ? (show work/why)

4. For what number of miles does the probability become 80% that a randomly selected pump will no longer be effective? (show how assessed/why)

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