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The foreman of a bottling plant has observed that the amount of soda pop in each 32 ounce bottle is actually a normally distributed random variable with?

1.  The foreman of a bottling plant has observed that the amount of soda pop in each 32 ounce bottle is actually a normally distributed random variable with? = 32.2 ounces and? = .3 ounces.
 
a.      Find the probability that if a customer buys one bottle, it will contain at least 32 ounces.
 
z = (32-32.2) / .3 = - 0.6666
z < 0.6666
z = .2454  
 
b.     Find the probability that if a customer buys a carton of four bottles, the mean will be at least 32 ounces.
 
z = (32 - 32.2 (4) / .3 = - 322.666?
 
3. A random sample of 200 SJU undergraduate students was asked if we should cancel classes that evening due to snowy weather. 112 students said yes.  So, can we say majority (i.e. greater than 50%) of students believe we should cancel class
 
                        Yes, a majority. P = 50, z value of .50 = .1915
(x - 200) / 112 - .1915
 x = 1.5942
 
5. The number of days it takes to build a new house has a variance of 226. A sample of 36 new homes shows an average building time of 83 days. What is the percent chance can we assert that the average building time for a new house is between 80 and 89 days.
 
6.  Time spent using e-mail per session is normally distributed, with µ=8 minutes and ?=2 minutes. If you select a random sample of 25 sessions,
a.      what is the probability that the sample mean is between 7.8 and 8.2 minutes?
(7.8 - 8.2) /  (8/2)
b.      what is the probability that the sample mean is between 7.5 and 8 minutes?
c.      if you select a random sample of 100 sessions, what is the probability that the sample mean is between 7.8 and 8.2 minutes?
d.     Explain the difference in the results of (a) and (c).
 
7.  In an online survey of 4,001 respondents, 8% were classified as productivity enhancers who are comfortable with technology and use the Internet for its practical value. Suppose you select a sample of 400 students at your school, and the population proportion of productivity enhancers is 0.08.
a.      What is the probability that in the sample, fewer than 10% of the students will be productivity enhancers?
 
b.     What is the probability that in the sample, between 6% and 10% of the students will be productivity enhancers?
 
c.      What is the probability that in the sample, more than 5% of the students will be productivity enhancers?
 
If a sample of 100 is taken, how does this change your answers?

Solution Preview

1. The foreman of a bottling plant has observed that the amount of soda pop in each 32 ounce bottle is actually a normally distributed random variable with ? = 32.2 ounces and ? = .3 ounces.

a. Find the probability that if a customer buys one bottle, it will contain at least 32 ounces.

z = (32-32.2) / .3 = - 0.6666
z < 0.6666
z = .2454
You are right in your process to obtain the value of z.
To get the probability, we need to get the probability value that corresponds to -0.67 in the z table.
P(z>-0.67)=1-0.2514=0.7486

b. Find the probability that if a customer buys a carton of four bottles, the mean will be at least 32 ounces.

z = (32 - 32.2 (4) / .3 = - 322.666?

Z=(32-32.2)/(0.3/sqrt(4))=-1.33
P(z>-1.33)=1-0.0918=0.9082

3. A random sample of 200 SJU undergraduate students was asked if we should cancel classes that evening due to snowy weather. 112 students said yes. So, can we say majority (i.e. greater than 50%) of students believe we should cancel class

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