Question

The graph shows the distribution of the number of text messages young adults send per day. The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 30 messages.

What percentage of young adults send more than 158 text messages per day?

16%
34%
68%
84%

Answer 1

Answer:

16%

Step-by-step explanation:

Answer 2

From the graph of distribution of the number of text messages

Young adults send more than 158 text messages per day is 16%

Given :

The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 30 messages.

Given 158 text messages . so x is 168

Now we find out z -score

$z=\frac{x-mean}{standard\; deviation }$

Replace the values and find out z

$z=\frac{158-128}{30} =1$

the value of z=1

Lets use the standard deviation table that gives area on the left

the table gives the percentage of adults less than 158

z-score value for z=1 is 0.8413

Now, percentage of young adults send more than 158 text messages  

Percent (more than 158)=1- P(less than 158)=$1-0.8413=0.1587$

To get percentage we multiply by 100

$0.1587 \cdot 100= 15.87= 16$

Young adults send more than 158 text messages per day is 16%

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