Suppose that 53% of all cars on interstate highways have one occupant (the drive

Question

Suppose that 53% of all cars on interstate highways have one occupant (the driver). Assume repeated random samples of 400 cars are examined, and a sample proportion of one-occupant cars is calculated for each sample. a) What will the mean of the sample proportions be? (percent form) _____ b What will the standard deviation of the sample proportions be? (percent form) _____ c) Use the Empirical Rule to find the interval in which the sample proportions will fall 95% of the time. (percent form) _____ Suppose that the actual mean Wechsler IQ score is 110 and the standard deviation is 24. Using Table 8.1: a) Find the probability that a person selected at random has an IQ score below 116. _____ b) Find the probability that the mean IQ score for a sample of 36 people is below 116. _____ e) What is the standard deviation of the sample mean IQ score for a sample of size 36?

Explanation / Answer

a) mean =0.53

b)std deviation =(p(1-p)/n)1/2 =0.025

c) as per emirical rule 95% value fall with in 2 standard deviation from mean

hence interval =0.48 ; 0.58

2)a) P(X<116) =P(Z<(116-110)/24)=P(Z<0.25)=0.5987

b)for n=36; std error =std deviation/(n)1/2 =4

P(X<116) =P(z<(116-110)/4)=P(Z<1.5)=0.9332

c) std deviation of mean = population std deviation/(n)1/2 =4

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