Do2 a,b,c,d 2. The distribution of the number of violent crimes per day in a cer

Question

Do2 a,b,c,d

2. The distribution of the number of violent crimes per day in a certain city possesses a mean of 1.3 and a standard deviation of 1.7. A random sample of 50 days is observed, and the mean number of crimes for this sample, y, is calculated. a) Could the population consisting of the number of violent crimes in a single day in this city be normally distributed? Explain. Will the sampling distribution of the sample mean be approximately normally distributed? Explain. b) Give the mean and the standard error of the sampling distribution of y. c) Find the probability that the sample mean y will be less than 1 crime per day. d)

Explanation / Answer

a) NO as crime can not be less then 0 ; which is less then 1 std deviation away from mean which indicate that distribution is not symmetric but skewed

b) from central limit theorum as sample size is greater then 30 ; tehrefore sampling distribution of sample mean is aproximately normal

c) mean of sampling distrbution of Ybar =1.3

and std error =std deviation/(n)1/2 =1.7/(50)1/2 =0.2404

d) probability that sample mean is less then 1 crime per day =P(Ybar<1) =P(Z<(1-1.3)/0.2404)

=P(Z<-1.2478)=0.1060

please revert for any clarificaiton

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