Statistics and Probability Answers

An electronic system has four components labeled as 1, 2, 3, and 4. The system has to be used during a given time period. The probability that component i will fail during that time period is fi for i = 1, . . . , 4. Failures of the components are physically independent of each other. A system failure occurs if component 1 fails or if at least two of the other components fail. Specify an appropriate sample space and determine the probability of a system failure.

1)     Recent business graduates currently employed in full-time positions were surveyed. Family backgrounds were self-classified as relatively high or low socioeconomic status. For a random sample of 16 high- socioeconomic status recent business graduates, mean total compensation was $34500 and the sample standard deviation was $8520. For an independent random sample of 9 low-socioeconomic status recent business graduates, mean total compensation was $31,499 and the sample standard deviation was $7,521.

A)   Find a 90% confidence interval for the difference between the two populations means. 

B)    Test at 1% level of significance the means of the two populations are not equal.

calculate the X2 and test whether the two attributes are independent at 5% level of significance

a random sample of 150 worker with children in day care show a man day a care cost of r. s 3700 a standard deviation is r. s 600 verified the department claim that the mean is equal to r. s3500 at the 0.05 level of significance

calculate the X2 and test whether the two attributes are independent at 5% level of significance

Supppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interest us.

• Suppose n =33 and p=0.20. Can we approximate p^ by a normal distribution?why? Np=
• Nq=

A factory manufactures cars with a warranty of 5 years on the engine and transmission.  An engineer believes that the engine or transmission will malfunction in less than 5 years.  He tests a sample of 40 cars and find the average time to be 4.8 years with a standard deviation of 0.50. At a 2% confidence level, is there enough evidence to support the idea that the warranty should be revised ?  ( P-value Test)

26789*6666

Suppose the quarterly sales for a particular make of a car in Delhi were 2682, 2462

and 3012, respectively. From the past data prior to these three data points, a straight

line was to fit. The value on the line corresponding to the last observed time is 2988

and the slope is 80. Use exponential smoothing based upon the three observations

given above to forecast sales for the quarterly period following these observations,

using α = β = 0 ⋅ .2

The mean arrival rate to a service centre is 3 per hour. The mean service time is found 

to be 10 minutes foe service. Assuming Poisson arrival and exponential service time, 

find

 (i) the utilisation factor for this service facility, 

 (ii) the probability of two units in the system, 

 (iii) the expected number of units in the system, and 

 (iv) the expected time in hours that a customer has to spend in the system.