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Venkat N.
Tutor withl 6 yrs Experience and working in IT in analytics
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Trigonometry
TutorMe
Question:

The average house price in Lincoln Park based on the random sample of 64 homes is $525,000. Your friend at the Chicago City Office tells you that the standard deviation of the house prices based on all houses in Lincoln Park is $80,000. Determine the 90% confidence interval

Venkat N.
Answer:

mean=525000 n=64 sd=80,000 z crit for 1.645 90% confidence interval. for population mean is sample mean-zcrit(population sd/sqrt(n),sample mean+zcrit(population sd/sqrt(n) 525000-1.645(80000/sqrt(64),525000+1.645(80000/sqrt(64) 508550,541450 508550<\displaystyle \mu<541450 lower limit=508550 upper limit=541450

Basic Math
TutorMe
Question:

How many different letter arrangements can be made from the letters Michigan?

Venkat N.
Answer:

MICHIGAN=7 letter word we have 2 I's No of different letter arrangements=7!/2! =7*6*5*4*3*2/2*1 =7*6*5*4*3 =2520 2520 ways of arrangement.

Statistics
TutorMe
Question:

A researcher randomly (no bias) selects 121 trees in the forest to measure the diameter of the trunk. If you know that the sample mean is 15 inches, and the standard deviation for the entire forest is 33 inches, what is the probability distribution of the sample mean. (Hint: Use Central Limit Theorem, which says that sample mean has a normal distribution with the mean same as population and standard deviation of population standard deviation divided by square root of the sample size

Venkat N.
Answer:

n=samplesize=`121 n>30 sample follows normal distruibution according to central limit theorem probability distribution is normal distribution sample mean=pop mean=15 standard error=samplesd/sqrt(n) =33/sqrt(121) =33/11 =3 standard error of sample mean=

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