Question

Which one of the following is not unbiased estimators

		Sample Variances
		Sample Means
		Sample Medians
		Sample Proportions

Adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that a randomly selected adult has an IQ that is greater than 115.

		0.3174
		0.1587
		0.2015
		0.8413

The random variable X has the following probability distribution.

x	0	1	2
P(x)	0.3	0.4	0.3

The variance of this distribution is

		0.1
		1.0
		1.6
		0.6

Answer 1

1). the option which is not an unbiased estimator is:-   sample median.

[ explanation:-

we know that sample mean, sample variance and sample proportions are all unbiased estimators, while, 'sample median' is supposed to be an unbiased estimator if population is normal or the distribution of population is symmetric.]

2).X: IQ scores of adults.

X ~ N(100,15)

the probability that a randomly selected adult has an IQ that is greater than 115 be:-

[ from standard normal table]

3).the table be:-

x
0	0.3	0	0
1	0.4	0.4	0.4
2	0.3	0.6	1.2
		sum=1	sum=1.6

the mean be:-

the variance of the distribution be:-

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