Math  /  Numbers & Operations

QuestionPoints: 0 of 1
Check here for instructional material to complete this problem. Evaluate μ=np\mu=n p for n=70n=70 and p=0.75p=0.75. Save \qquad \square μ=\mu=\square (Simplify your answer. Type an integer or a decimal. Do not round.)

Studdy Solution

STEP 1

What is this asking? We need to plug in the numbers n=70n = 70 and p=0.75p = 0.75 into the formula μ=np\mu = n \cdot p and calculate the result. Watch out! Make sure to multiply correctly and don't round the final answer!

STEP 2

1. Substitute the values
2. Calculate the result

STEP 3

We are given n=70n = 70 and p=0.75p = 0.75.
Remember, these represent the **number of trials** (nn) and the **probability of success** (pp) respectively.
It's like flipping a weighted coin 70 times, where the coin lands heads with a probability of 0.75!

STEP 4

Let's substitute these values into our formula μ=np\mu = n \cdot p.
This gives us μ=700.75\mu = 70 \cdot 0.75.
We're almost there!

STEP 5

Now, let's **multiply** 7070 by 0.750.75.
Think of it as 70 times 75 cents. 700.75=52.570 \cdot 0.75 = 52.5.

STEP 6

So, our **final result** is μ=52.5\mu = 52.5.
This μ\mu represents the **expected value**, or the average number of successes we'd expect to see if we repeated this experiment many times.
In our coin-flipping example, we'd expect to get heads roughly 52.5 times out of 70 flips, on average.

STEP 7

μ=52.5\mu = 52.5

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