Help solve and show steps please thank you. Write the symbol, number, or word th

Question

Help solve and show steps please thank you. Write the symbol, number, or word that best answers the question. Provide numerical answers as exact values (fractions are okay), or round to 3 significant decimal places. A soda machine dispenses normally distributed amounts of soda with a mean of 20 ounces and a standard deviation of 0.2 ounce. Are you more likely to randomly select one bottle with an amount between 19.8 ounces and 20.2 ounces or are you more likely to select a sample of, eight bottles with a mean amount between 19.8 ounces and 20.2 ounces? Explain. A study of 800 homeowners in a certain area showed that the average value of the homes is $182,000 and the standard deviation is $15,000. If 50 homes are for sale, find the probability that the mean value of these homes is greater than $185,000. Remember, check to see if the finite correction factor applies.

Explanation / Answer

20) From information given, Xbar=20, s=0.2, Xi=19.8 and 20.2. Substitute valuesin following equation to obtain the z scores.

z1=(Xi-Xbar)/s=(19.8-20)/0.2=-1 and z2=(20.2-20)/0.2=1

P(19.8<X<20.2)=P(-1<z<1)=0.3413+0.3413=0.6826

Now, if sample size is increased from 1 to 8, it will give better precision with decreased interval width.

21. Xbar=182,000, Xi=185,000,s=15,000

z=(185000-182000)/15000=0.2

P(X>185,000)=P(z>0.2)=0.4207

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