i need someone to explain these to me please

i've looked through the book, and feel like i know how to do them, but need help. im pretty sure about 9, i got .8^6 and .2^6 and so on, but some help with explanations would be great, i'm lost. i finished everything but those.


9). the fbi standard survey of crimes showed that for avout 80% of all crimes the criminals are never found and the case is never solved. suppose in a neighborhood the police are investigating 6 property crimes. consider success when a case is solved and the criminals are found.
a) what is the probability that none of the crimes will ever be solved?
b) what is the probability that all the crimes will be solved?
c) what is the expected number of crimes that will be solved? what is the standard deviation?
d) graph the probability distribution and determine if it is a probability distribution of a continuous or a discrete variable.

10). Let x be a random variable representing the amount of sleep each adult in New York City got last night. All we know about x-distribution is that it has a mean ? = 7 and standard deviation ? = 3. consider a sampling distribution of sample mean xbar for sample size n =36.

a) what can you say about the xbar- distribution?
b) what value will the standard deviation ? (to the xbar power) of the sampling distribution approach? what is its mean?
c) find P(xbar< 6), P(xbar> 7) and P(6.5<xbar<7.5).
d) assuming that x is normally distributed, find the standardized score of an adult in NYC who got 3 hours of sleep.

11). A sample of the assets (in millions of dollars) of 30 credit unions in Southwestern Pennsylvania has a mean xbar= 11.091 and standard deviation s= 14.405.

a)Find the 90% confidence interval of the mean of ?.
b) assuming that the standard deviation of all the assets (in millions of dollars) of all credit unions in southwestern pennsylvania is ? = 12, find a 95% confidence interval of the mean of ?.

12). Gentle Ben is a morgan horse at a Colorado Ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml)

93 88 82 105 99 110 84 89

the sample mean is xbar = 93.8. Let x be a random variable representing glucose readings taken from the horse. we may assume that x has a normal distribution, with ? = 85 mg/100ml and ? = 12.5. use ? = 0.05.
use the hypothesis testing to check if this sample data indicates that gentle ben has an overall average glucose level higher than 85? use ? = 0.05.

For Q9(c), the expected number of crimes solved is
0(P[sub:2tk1tc0i]0[/sub:2tk1tc0i])+1(P[sub:2tk1tc0i]1[/sub:2tk1tc0i])+2(P[sub:2tk1tc0i]2[/sub:2tk1tc0i])+3(P[sub:2tk1tc0i]3[/sub:2tk1tc0i])+4(P[sub:2tk1tc0i]4[/sub:2tk1tc0i])+5(P[sub:2tk1tc0i]5[/sub:2tk1tc0i])+6(P[sub:2tk1tc0i]6[/sub:2tk1tc0i]).
The expected number is the mean, which is each individual amount times it's expected value.

The standard deviation is then square root of the average of the "deviations squared".
You can calculate that when you have the mean.

(d) number of crimes is a natural number... discrete.

Q10 (a) Irrespective of the shape of the population distribution, what is the sampling distribution,
refer to the Central Limit Theorem.
(b) The population has mean = 7 and SD = 3.
For a sample, you must answer "is the mean the same or different and what is the new SD calculated using n" ?

(c) and (d) should be do-able then.