The brand manager for a brand toothpaste must plan a campaign designed to increase brand recognition. he wants to first determine the percentage of adults wii have heard of the brand. how many adults must he survey in order to be 90%confident that hiss estimate is within five percentage points off the true population percentage?

We need to find out how many adults must the brand manager survey in order to be 90% confident that his estimate is within five percentage points of the true population percentage.

From the given data we know that our confidence level is 90%. From Standard Normal Table we know that the critical level at 90% confidence level is 1.645. In other words, .

We also know that E=5% or E=0.05

Also, since, is not given, we will assume that =0.5. This is because, the formula that we use will have in the expression and that will be maximum only when =0.5. (For any other value of , we will get a value less than 0.25. For example if, is 0.4, then and thus, .).

We will now use the formula

We will now substitute all the data that we have and we will get

which can approximated to n=271.

So, the brand manager needs a sample size of 271

The brand manager needs a sample size of 271

Step-by-step explanation:

Given: The brand manager for a brand toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults Wii have heard of the brand.

As per question:

We have to find out how many adults must the brand manager survey in order to be confident that his estimate is within points of the true population percentage.  

As we know that

Now, the value of sample size is calculated as

We can approximate the value of to .

Therefore, the brand manager needs a sample size of .

Learn more about sample size here:

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168

step-by-step explanation:

first off, we know that he drove 3.5 hours at a rate of 48 mph.

knowing that, we want to see how many miles he drove all-together.

in this case, we can just multiply 48 by 3.5.

48 * 3.5 = 168

step-by-step explanation:

a cube has 6 sides

the probability of getting 5 on the first cube is 1/6 since only one side of the cube has 5 on it.

there are 3 sides of the cube with even number on it [2,4,6]

therefore the probability of getting even number is 3/6

for both events to happen together, the probability would be

1/6 x 3/6 = 12/36

which simplifies to 1/12