Question

The amount of time people spend exercising in a given week follows a normal distribution with a mean of 3.8 hours per week and a standard deviation of 0.8 hours per week.
i) Which of the following shows the shaded probability that a person picked at random exercises less than 2 hours per week?
ii) What is the probability that a person picked at random exercises less than 2 hours per week? (round to 4 decimal places)
iii) Which of the following shows the shaded probability that a person picked at random exercises between 2 and 4 hours per week?
iv) What is the probability that a person picked at random exercises between 2 and 4 hours per week? (round to 4 decimal places)

Answer 1

Answer:

i and iii) In the figure attached part a we have the illustration for the area required for the probability of less than 2 hours and in b the illustration for the probability that X would be between 2 and 4

ii) $P(X$

And using the normal standard table or excel we got:

$P(z$

iv) $P(2$

And we can find the probability with the following difference and usint the normal standard distirbution or excel and we got:

$P(-2.25$

Step-by-step explanation:

Let X the random variable that represent amount of time people spend exercising in a given week, and for this case we know the distribution for X is given by:

$X \sim N(3.8,0.8)$  

Where $\mu=3.8$ and $\sigma=0.8$

Part i and iii

In the figure attached part a we have the illustration for the area required for the probability of less than 2 hours and in b the illustration for the probability that X would be between 2 and 4

Part ii

We are interested on this probability:

$P(X$

We can use the z score formula given by:

$z=\frac{x-\mu}{\sigma}$

Using this formula we have:

$P(X$

And using the normal standard table or excel we got:

$P(z$

Part iv

We want this probability:

$P(2$

Using the z score formula we got:

$P(2$

And we can find the probability with the following difference and usint the normal standard distirbution or excel and we got:

$P(-2.25$