The amount of cola in a 355 ml bottle from a certain company is a random variable with a mean of 355 ml and a standard deviation of 2 ml. for a sample of size 32, perform the following calculations. a. find an approximate probability that the sample mean is less than 354.8 ml. b. suppose the amount of cola is distributed as n(355, 4). find an approximate probability that 10 of the bottles in the sample contain less than 354.8 ml of cola.

a)

b)

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent the amount of cola in a 355 ml bottle from a certain company, and for this case we know the distribution for X is given by:

And let represent the sample mean, the distribution for the sample mean is given by:

On this case  

Part a

We want this probability:

The best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

Part b

Let X the random variable that represent the amount of cola in a 355 ml bottle from a certain company, and for this case we know the distribution for X is given by:

And let represent the sample mean, the distribution for the sample mean is given by:

On this case  

We want this probability:

The best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

The answer is in the image 

The solution is in the following image

The answer is in the image 

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

The solution is given in the image below

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.