Answer:
DC = 10.93 cm , AC = 9.8 cm
Step-by-step explanation:
From trigonometry;
⇒ Tan 60 = AB/BD
⇒AB = BD Tan 60 ( where BD = 4 cm )
⇒ AB = 6.93 cm
Also, AB=BC , therefore;
⇒ BC = 6.93 cm
⇒ Cos 60 = BD/AD
⇒ AD = BD/ Cos 60 = 4/Cos 60
⇒ AD = 8 cm
From Pythagoras theorem;
⇒ =
+
=
+
⇒ AC = = 9.80 cm
⇒ DC = BD + BC = 4 + 6.93
⇒ DC = 10.93 cm
We have been given that the distribution of the number of daily requests is bell-shaped and has a mean of 38 and a standard deviation of 6. We are asked to find the approximate percentage of lightbulb replacement requests numbering between 38 and 56.
First of all, we will find z-score corresponding to 38 and 56.
Now we will find z-score corresponding to 56.
We know that according to Empirical rule approximately 68% data lies with-in standard deviation of mean, approximately 95% data lies within 2 standard deviation of mean and approximately 99.7% data lies within 3 standard deviation of mean that is .
We can see that data point 38 is at mean as it's z-score is 0 and z-score of 56 is 3. This means that 56 is 3 standard deviation above mean.
We know that mean is at center of normal distribution curve. So to find percentage of data points 3 SD above mean, we will divide 99.7% by 2.
Therefore, approximately of lightbulb replacement requests numbering between 38 and 56.