Question

Question 6 3 pts The number of violent crimes committed in a day possesses a distribution with a mean of 3.5 crimes per day and a standard deviation of 4 crimes per day. A random sample of 100 days was observed, and the mean number of crimes for the sample was calculated. Describe the sampling distribution of the sample mean. shape unknown with mean = 3.5 and standard deviation = 0.4 shape unknown with mean = 3.5 and standard deviation-4 approximately normal with mean = 3.5 and standard deviation - 0.4 approximately normal with mean = 3.5 and standard deviation - 4 Question 7 3 pts Furnace repair bills are normally distributed with a mean of 269 dollars and a standard deviation of 20 dollars. If 49 of these repair bills are randomly selected, find the probability that they have a mean cost between 265 dollars and 271 dollars. 0.1191 0.3227 0.6773 0.7800

Answer 1

$\\ The\ shape\ is\ approximately\ normal\\ \\ mean =3.5\\ \\ standard\ deviation =\frac{4}{\sqrt{100}}=\frac{4}{10}=0.4\\ \ So,\ correct\ choice\ is \\$

approximately normal with mean = 3.5 and standard deviation - 4

$\\ 7)\ mean\ of\ sampling\ distribution =269\\ \\ standard\ deviation\ of\ sampling\ distribution =\frac{20}{\sqrt{49}}=2.8571$

P(265<X̅<271)

=P((265-269)/2.8571<Z<(271-269)/2.8571)

=P(-1.4<Z<0.7)

=P(Z<0.7)-P(Z<-1.4)

=0.758-0.0808

=0.6772

0.6773