Mean and standard deviation of sample proportions

Suppose that 35% of students in a school can sing their national anthem correctly. The music teacher takes an SRS of 30 students from the population of 750 students at the school and finds that 40% of students sampled can sing their national anthem correctly. The teacher plans to take more samples like this. Let p represent the proportion of a sample of 30 students in the school who can sing their national anthem correctly. What are the mean and standard deviation of the sampling distribution of p?​

Answer: D

Suppose that 35\%35%35, percent of students in a school can sing their national anthem correctly. The music teacher takes an SRS of 303030 students from the population of 750750750 students at the school and finds that 40\%40%40, percent of students sampled can sing their national anthem correctly. The teacher plans to take more samples like this.

Step-by-step explanation: Khan Academy Explanation

The mean and standard deviation is given by -

μ = 0.35 and σ = 0.09.

Given is that suppose that 35% of students in a school can sing their national anthem correctly. The music teacher takes an SRS of 30 students from the population of 750 students at the school and finds that 40% of students sampled can sing their national anthem correctly. The teacher plans to take more samples like this. Let {p} represent the proportion of a sample of 30 students in the school who can sing their national anthem correctly.

        where -

        {σ} = population standard deviation

        {N} = the size of the population

        x{i} = each value from the population

        {μ} = the population mean

The mean and standard deviation is given by -

μ = 0.35

σ = √(0.35)(0.65)/(30) = 0.48/5.5 = 0.09

σ = 0.09

Therefore, the mean and standard deviation is given by -

μ = 0.35 and σ = 0.09

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