Question

Sales records indicate that the selling price of used cars at a large car dealership are skewed right, with a mean of $17000 and a standard deviation of $11000 Explain whether Table Z (the normal distribution table) could be used to find the probability that a single used car at this dealership would sell for less than $20000

Answer 1

Ans! Let X be a random variable indicates that the selling price ad used cars at a large dealership Given that population mean: 4 = $17000 population standard deviation : 6 = $$11000 we Here have to find the probability that a single used car at this dealership would sell for less than $20000 i-e. To frnd Plx< 20000) Thus to evaluate this probability we need to convert it in toomo of NCO,1) by using toansfoomation X- Z q 20000-e : p(x-4 -4)= Plze 20000-17000 110 do - P(Z20.27) where 2= x- uNllon) .:|[<20000) = 0.6064 (from noomal table) :: The probability that a single used car at this dealership would sell for less than $ 20000 is 0.6064

Here we have sample size = 70 We know that for sampling distoibution: mean of is y & standard deviation of it is sila average * The mean for the sampling distribution of price would be & standata deviation is 427000 DE E sila 11000 170 - 1314.75 : The mean for the sampling distribution d average price would be $17000 & the standard deviation would be 1314.75

from central limit theorem The sample size Assumption are the sample size must be sufficiently large. In general a sample size of 30 is considered sufficient if the sample is unimodal Here sample size = 70 Since the sample size assumption for the cento al limit theorem is satisfied,

We know that from the Empirical Rule Approximately 687- of the data lie within one standard deviation of the mean ie the interval endpoints Its =The interval endpoints 19000 - 1314.73 and 14000 11314.75 *( 15685,25 and 18314.75) for a random sample a 70 prices for used cars that are sold there is a 684. probability the mean price of the 10 cars falls between 15685.25 and 18314.75