A sample of size will be drawn from a population with mean and standard deviation . Use the TI-84 calculator. Part 1 of 2 Find the probability that will be more than . Round the answer to at least four decimal places. The probability that will be more than is . Part 2 of 2 Find the percentile of . Round the answer to two decimal places. The percentile is .

A sample of size 50 will be drawn from a population with mean 12 and standard deviation 8 . Use the TI-84 calculator.

- Find the probability that x will be more than 10 . Round the answer to at least four decimal places.

- Find the 45th percentile of μ. Round the answer to two decimal places.

Answers

The T1-84 calculator answer are

- 0.9614

- 11.84

However, without using the T1-84 calculator, the answers are

- 0.9616

- 11.87

Explanation:

Given that

Sample size = n = 50

Population mean = μ = 12

Standard Deviation = σ = 8

a. Here, we're to calculate the probability that the sample mean is greater than 10.

i.e P(X>10)

To do this, we'll calculate z - value using the following formula.

Z = (x - μ)/(σ/√n)

By substituton

Z = (10 - 12)/(8/√50)

Z = -1.77 Approximately

The value of P(X > 10) is calculated by P(Z > -1.77)

So, P(X > 10) = P( Z > -1.77)

P(X>10) = P(Z<1.77)

P(X>10) = 0.961636

P(X>10) = 0.9616 Approximated

b. Here, we're to calculate the 45th percentile of the population mean.

To do that, we'll make use of this formula

X=μ + Z, and we will use the standard normal distribution table.

Where μ = Population mean = 12

Z = the corresponding z score of 45th percentile

From z table, 45th percentile = -0.126

By substituton

X = μ + Zσ becomes

X = 12 + (-0.126*1)

X = 11.874

X = 11.87 --- Approximately

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