00:01
In this problem, random variable x will be the height of a certain population of corn plant.
00:10
And we know that x follows the normal distribution.
00:17
Population mean mu is 145 cm, and population standard deviation sigma is 22 cm.
00:29
Task a.
00:31
We should find the percentage of the plants that are between 135 and 155 cm tall.
00:42
So now let's find the probability that x will be between 135 and 155.
00:55
This equals to probability that x is less than 155 minus probability that x is less than 135.
01:12
After this, we obtain probability that z -score is less than 155 minus population mean 145 divided by standard deviation 22 minus probability that z -score is less than 135 minus 145 divided by 22.
01:42
And we obtain probability that z -score is less than 0 .455 rounded to three decimal places minus probability that z -score is less than minus 0 .455.
02:05
And now by using z -score table, we can find the corresponding probabilities.
02:16
0 .67454 minus 0 .3246.
02:26
And we obtain 0 .3508...