Given:
μ = 25 mpg, the population mean
σ = 2 mpg, the population standard deviation

If we select n samples for evaluation, we should calculate z-scores that are based on the standard error of the mean.
That is,
$z= \frac{x-\mu}{\sigma / \sqrt{n} }$

The random variable is x = 24 mpg.

Part (i): n = 1
σ/√n = 2
z = (24 -25)/2 = -0.5
From standard tables,
P(x < 24) = 0.3085

Part (ii): n = 4
σ/√n = 1
z = (24 -25)/1 = -1
P(x < 24) = 0.1587

Part (iii): n=16
σ/√n = 0.5
z = (24 - 25)/0.5 = -2
P(x < 24) = 0.0228

Explanation:
The larger the sample size, the smaller the standard deviation.
Therefore when n increases, we are getting a result which is closer to that of the true mean.

6 0

3 years ago

Find the value of the polynomial 5x – 4x^2 + 3 at x = 2 and x = –1

aliya0001 [1]

Answer:

Let the polynomial be f(x) = 5x – 4x^2 + 3

Now, for x = 2,

f(2) = 5(2) – 4(2)^2 + 3

=> f(2) = 10 – 16 + 3 = –3

Or, the value of the polynomial 5x – 4x^2 + 3 at x = 2 is -3.

Similarly, for x = –1,

f(–1) = 5(–1) – 4(–1^)2 + 3

=> f(–1) = –5 –4 + 3 = -6

The value of the polynomial 5x – 4x2 + 3 at x = -1 is -6.

Answered by GAUTHMATH

6 0

2 years ago

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