In a certain class 27% of the students are left-handed. suppose that a random sample of 53 students is selected. Find the mean number of left-handed students in the class. Round your answer to the nearest integer.
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To find the mean number of left-handed students in the class, we need to multiply the total number of students in the class by the percentage of left-handed students.
Step 1: Convert the percentage to a decimal: 27% = 0.27.
Step 2: Multiply the decimal by the total number of students: 0.27 * 53 = 14.31.
Step 3: Round the answer to the nearest integer: rounding 14.31 to the nearest integer gives us 14.
Therefore, the mean number of left-handed students in the class is 14.
To find the mean number of left-handed students in the class, you can use the concept of expected value. The expected value is the average result you would expect to obtain if you repeated the sampling process many times.
Here's how you can calculate the mean number of left-handed students in the class:
1. Find the probability of a single student being left-handed. Given that 27% of the students are left-handed, the probability of a single student being left-handed is 0.27.
2. Multiply the probability of a single student being left-handed by the total number of students in the sample. In this case, the sample size is 53.
Expected value = Probability of left-handed student * Sample size
Expected value = 0.27 * 53
3. Calculate the expected value by multiplying the probability by the sample size.
Expected value = 14.31
4. Finally, round the expected value to the nearest integer.
Mean number of left-handed students = 14
Therefore, the mean number of left-handed students in the class is 14.