A random sample of 144 observations has a mean of 20, a median of 21, and a mode of 22. The population standard deviation is known to equal 4.8. The 95.44% confidence interval for the population mean is .

95.44% confidence interval for the population mean is [19.2 , 20.8].

Step-by-step explanation:

We are given that a random sample of 144 observations has a mean of 20, a median of 21, and a mode of 22. The population standard deviation is known to equal 4.8.

Also, assuming that the data follows normal distribution.

So, the pivotal quantity for 95.44% confidence interval for the population mean is given by;

            P.Q. = ~ N(0,1)

where, = sample mean = 20

            = population standard deviation = 4.8

            n = sample of obs. = 144

            = population mean

So, 95.44% confidence interval for the population mean, is ;

P(-1.9991 < N(0,1) < 1.9991) = 0.9544

P(-1.9991 < < 1.9991) = 0.9544

P( < < ) = 0.9544

P( < < ) = 0.9544

95.44% confidence interval for = [ , ]

                                                       = [ , ]

                                                       = [19.2 , 20.8]

Therefore, 95.44% confidence interval for the population mean is [19.2 , 20.8].

step-by-step explanation:

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