# Math Help - Probability help

1. ## Probability help

Hi im someone who is a strugglnig a little with the statistics part of his course! I have a couple of question and would be very grateful if someone could answer.
I struggle a bit with turning equation into practical usage so if i see the working needed I will probably clock onto the concept very fast.

'Information of a packet of seeds says the germination rate is 92%, what is the probability that 95% of seeds in the packet of 160 will germinate?'

'The weight of a pakcet of crisps is 10 ounces, the amount that the packaging machene puts in these bags is beleived to have a normal model10.2 and a standard deviation 0.12 ounces
a) what fraction of all bags sold are underweight
b) what is the probablity that of a multipack fo 3 none are underweight
c) what is the probability that the mean weight of the 3 bags is below the stated amount
d) whats the probability that the mean weight of a 24 bag box of crisps is below 10 ounces

2. Originally Posted by AndrewFFC
Hi im someone who is a strugglnig a little with the statistics part of his course! I have a couple of question and would be very grateful if someone could answer.
I struggle a bit with turning equation into practical usage so if i see the working needed I will probably clock onto the concept very fast.

'Information of a packet of seeds says the germination rate is 92%, what is the probability that 95% of seeds in the packet of 160 will germinate?'

[snip]
Let X be the random variable number of seeds that germinate.

X ~ Binomial(n = 160, p = 0.92)

Calculate $\Pr(X \geq 152)$.

You could probably use the normal approximation to the binomial distribution to get the asnwer.

3. Originally Posted by AndrewFFC
[snip]

'The weight of a pakcet of crisps is 10 ounces, the amount that the packaging machene puts in these bags is beleived to have a normal model10.2 and a standard deviation 0.12 ounces
a) what fraction of all bags sold are underweight
b) what is the probablity that of a multipack fo 3 none are underweight
c) what is the probability that the mean weight of the 3 bags is below the stated amount
d) whats the probability that the mean weight of a 24 bag box of crisps is below 10 ounces
a) Calculate Pr(X < 10) = Pr(Z < 5/3) where the Z-value is found from $Z = \frac{X - \mu}{\sigma}$. I imagine you'll use either tables or technology.

b) If the answer to a) is p, then the answer here is (1 - p)^3.

c) The mean weight $\overline{X}$ follows a normal distribution with $\mu = 10.2$ and $\sigma = \frac{0.12}{\sqrt{3}}$. Use this normal distribution to calculate $\Pr(\overline{X} < 10)$.

d) The mean weight $\overline{X}$ follows a normal distribution with $\mu = 10.2$ and $\sigma = \frac{0.12}{\sqrt{24}}$. Use this normal distribution to calculate $\Pr(\overline{X} < 10)$.