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(solution) Airline passengers arrive randomly and independently at the


Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 8 passengers per minute.


aCompute the probability of no arrivals in a one-minute period (to 6 decimals).

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c

dCompute the probability that three or fewer passengers arrive in a one-minute period (to 4 decimals).

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f

gCompute the probability of no arrivals in a 15-second period (to 4 decimals).

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i

j

Compute the probability of at least one arrival in a 15-second period (to 4 decimals).A Randstad/Harris interactive survey reported that 25% of employees said their company is loyal to them (USA Today, November 11, 2009). Suppose 10 employees are selected randomly and will be interviewed about company loyalty.

Round your answers to four decimal places.

a.  Is the selection of ten employees a binomial experiment?

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Explain.

The input in the box below will not be graded, but may be reviewed and considered by your instructor.




b.  What is the probability that none of the 10 employees will say their company is loyal to them?

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c.  What is the probability that four of the 10 employees will say their company is loyal to them?

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d.  What is the probability that at least two of the 10 employees will say their company is loyal to them?

placeholder for rejoinderPlaceholder_2017097663_5_2017097663Twenty-three percent of automobiles are not covered by insurance (CNN, February 23, 2006). On a particular weekend, 35 automobiles are involved in traffic accidents.

aWhat is the expected number of these automobiles that are not covered by insurance (to the nearest whole number)?What is the variance and standard deviation (to 2 decimals)?

Variance

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Standard deviationAirline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 8 passengers per minute.


aCompute the probability of no arrivals in a one-minute period (to 6 decimals).

bplaceholder for rejoinderPlaceholder_1941802587_1_1941802587 

c

dCompute the probability that three or fewer passengers arrive in a one-minute period (to 4 decimals).

eplaceholder for rejoinderPlaceholder_1941802587_2_1941802587 

f

gCompute the probability of no arrivals in a 15-second period (to 4 decimals).

hplaceholder for rejoinderPlaceholder_1941802587_3_1941802587 

i

jCompute the probability of at least one arrival in a 15-second period (to 4 decimals).

kplaceholder for rejoinderPlaceholder_1941802587_4_1941802587The National Safety Council (NSC) estimates that off-the-job accidents cost U.S. businesses almost $200 billion annually in lost productivity (National Safety Council, March 2006). Based on NSC estimates, companies with 50 employees are expected to average three employee off-the-job accidents per year. Answer the following questions for companies with 50 employees.

aWhat is the probability of no off-the-job accidents during a one-year period (to 4 decimals)?

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c

dWhat is the probability of at least two off-the-job accidents during a one-year period (to 4 decimals)?

eplaceholder for rejoinderPlaceholder_731096718_2_731096718 

f

gWhat is the expected number of off-the-job accidents during six months (to 1 decimal)?

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i

jWhat is the probability of no off-the-job accidents during the next six months (to 4 decimals)?

kplaceholder for rejoinderPlaceholder_731096718_4_731096718In October of 2012, Apple introduced a much smaller variant of the Apple iPad, known at the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of 10.25 hours (The Wall Street Journal, October 31, 2012). Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.

a.  Give a mathematical expression for the probability density function of battery life.


a.b.c.The correct answer is:

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b.  What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

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c.  What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

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d.  What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

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e.  In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?

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