I would like to check myself if following my answer is correct: let us consider following problem:
Suppose the heights of a population of $3,000$ adult penguins are approximately normally distributed with a mean of $65$ centimeters and a standard deviation of $5$ centimeters.
(a) Approximately how many of the adult penguins are between $65$ centimeters and $75$ centimeters tall?
(b) If an adult penguin is chosen at random from the population, approximately what is the probability that the penguin’s height will be less than $60$ centimeters? Give your answer to the nearest 0.05.
so as i know approximately $68$ or $2/3$ fall in the interval of $[\mu-\sigma,\mu+\sigma]$,approximately $96$ fall between $[\mu-2*\sigma,\mu+2*\sigma]$
and approximately $99$% fall between
$[\mu-3*\sigma,\mu+3*\sigma]$
now we are asked between $75$ and $65$,which is equal
$[\mu-2*\sigma,\mu+2*\sigma]$
this range,but in this case it is second half range,in this range it would be half of or $48$%,which means that number of penguins would be $3000*0.48=1440$ penguins would be,am i correct?
on (b), less then $60$ means that below $65-5$ or below $[\mu-\sigma]$ or $16$ percent would be fall in this interval,am i correct?please help me