Normal distribution definition help pls

Normal distribution
Comment upon the suitability of using the normal distribution to model each of the following
i)the number of banans in bunch
ii)the handspan of adult females
iii)the ages of cars in a ppark
can somebody pls explain what this mmean tnx in advance

The question asks whether a good model for each situation would be the normal distribution. As a rule of thumb, anything that varies over a large population is normally distributed.

I'm not sure I agree with that :/ Because you can have a large population which is heavily skewed. I think the best way to think of it is if there is equal chance of a piece of data being a set amount above the mean as there is the chance of it being the same amount below.

The normal distribution is a continuous distribution, This means it can only take continuous variables.

Continuous variables can take any value. For example height can take variables of 124.4544cm or it can take 124.2cm. However in any continuous distribution P(X=x) = 0.
So the probability of one randomly chosen person having 124cm as their height for a group of adults is

P(x=124cm) =0.

This is because there are an infinite amount of values that height can take. Continuous probabilities are usually worked from sets. I.e P(X>124cm).

Is the number of bananas in a bunch a continuous or discrete variable?

What if a set of data was discrete?

Then it could be a Binomial distribution, Poisson distribution or some other type of distribution that specializes in discrete values. It's worth noting that any Poisson, Normal or Binomial distribution can be approximated to each of the other types regardless of discrete or continuous data but each type of distribution is a better approximate than the others in certain scenarios.

For example, a Binomial distribution, X, is given by:

$X$~$Bi(100, 0.04)$

And I wish to calculate the probability of X being less than or equal to 60.

$Pr(X\leq60)$

This would be rather tedious to calculate in a Binomial distribution, but it becomes much easier to calculate if we approximate it to a Normal distribution. For this scenario, the Normal distribution was more suitable than the Binomial distribution.

Oh right ok.

So i'm thinking the bananas are discrete, am i right?

Oh right ok.

So i'm thinking the bananas are discrete, am i right?

Indeed, you can't have 4.526 of a banana now can you?

Unless bananas come in bunches of more than a hundred, in which case you can model them as being continuous (because the relative difference between 100 and 100.5 is 0 for approximation purposes).
My other reason for that not being normal is that most bunches that you can buy in a shop will have the same number of bananas, as part of quality regulation.

What about the age of cars in a car park? Would you count a car as 3 years old or 3.6 years old? I wouldn't know if this was discrete or continuous...

I'd say that in this example it would be continuous. Data from age is usually given in sets for statistics. I.e 0 - 4yrs, 5-10yrs etc and the last set will usually be something like 80+.

Having said that, if we were measuring age in a Year 5 classroom of 30 students where the ages of students tend to range from 9 to 11. We could regard this as discrete since we don't need to consider any ages below or above 9 to 11. No sets, just the discrete values of 9,10, or 11.