Height of dutch men. males in the netherlands are the tallest, on average, in the world with an average height of 183 centimeters (cm) (bbc news website). assume that the height of men in the netherlands is normally distributed with a mean of 183 cm and standard deviation of 10.5 cm. a.what is the probability that a dutch male is shorter than 175 cm? b. what is the probability that a dutch male is taller than 195 cm? c. what is the probability that a dutch male is between 173 and 193 cm? d. out of a random sample of 1000 dutch men, how many would we expect to be taller than 190 cm?

a)

b)

c)

d)

And using a calculator, excel ir the normal standard table we have that:

So for this case we expect anyone with a heigth higher than 190 cm in a random sample of 1000.

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".  

Part a

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

Where and

We are interested on this probability

And 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:

And we can find this probability with the normal standard table or with excel:

Part b

And we can find this probability with the normal standard table or with excel: using the complement rule

Part c

And 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:

And we can find this probability on this way:

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

Part d

Since the distributiion for X is normal then the distribution for the sample mean is also normal and given by:

And we eant this probability:

And using a calculator, excel ir the normal standard table we have that:

So for this case we expect anyone with a heigth higher than 190 cm in a random sample of 1000.

linearly: 8560 bacteria

exponentially: approximately 75233 bacteria

step-by-step explanation:

assuming it is not exponential (we would have some really complicated logarithms), let's say it is linear. then, after 5 hours, it increased by 1200 bacteria, so every hour it increases by 240 bacteria. this means that after 19 hours, we get 19 * 240 + 4000 bacteria or 3800 + 760 + 4000 = 7800 + 760 = 8560 bacteria.

because it says round your answer, i will do this exponentially (with a calculator, of course). first, we need to find how much it multiplies by every hour, by taking the 5th root of 52/40 or 13/10. this is approximately 0.167. we still need to add 1 to this, because we are multiplying by that number, not adding that amount of the number. now, we just calculate 4000 * (1.167)^19. use a calculator to get approximately 75232.6, or 75233.

7.3

step-by-step explanation: