Mathematics, 22.04.2020 01:10 katherineedwards1105

The mean of a population is 74 and the standard deviation is 16. The shape of the population is unknown. Determine the probability of each of the following occurring from this population. Appendix A Statistical Tables a. A random sample of size 34 yielding a sample mean of 76 or more b. A random sample of size 120 yielding a sample mean of between 73 and 75 c. A random sample of size 218 yielding a sample mean of less than 74.8

Answers: 1

Show answers

Answers

Answer from: emma6892

(a) P( $\bar X$ $\geq$ 76) = 0.2327

(b) P(73 < $\bar X$ < 75) = 0.5035

Step-by-step explanation:

We are given that the mean of a population is 74 and the standard deviation is 16.

Assuming the data follows normal distribution.

Let $\bar X$ = sample mean

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean = 74

$\sigma$ = standard deviation = 16

n = sample size

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

(a) Probability that a random sample of size 34 yielding a sample mean of 76 or more is given by = P( $\bar X$ $\geq$ 76)

P( $\bar X$ $\geq$ 76) = P( $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ $\geq$ $\frac{76-74}{\frac{16}{\sqrt{34} } }$ ) = P(Z $\geq$ 0.73) = 1 - P(Z < 0.73)

= 1 - 0.7673 = 0.2327

The above probability is calculated by looking at the value of x = 0.73 in the z table which has an area of 0.7673.

(b) Probability that a random sample of size 120 yielding a sample mean of between 73 and 75 is given by = P(73 < $\bar X$ < 75) = P( $\bar X$ < 75) - P( $\bar X$ $\leq$ 73)

P( $\bar X$ < 75) = P( $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{75-74}{\frac{16}{\sqrt{120} } }$ ) = P(Z < 0.68) = 0.75175

P( $\bar X$ $\leq$ 73) = P( $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ $\leq$ $\frac{73-74}{\frac{16}{\sqrt{120} } }$ ) = P(Z $\leq$ -0.68) =1 - P(Z < 0.68)

= 1 - 0.75175 = 0.24825

Therefore, P(73 < $\bar X$ < 75) = 0.75175 - 0.24825 = 0.5035

The above probability is calculated by looking at the value of x = 0.68 in the z table which has an area of 0.75175.

(c) Probability that a random sample of size 218 yielding a sample mean of less than 74.8 is given by = P( $\bar X$ < 74.8)

P( $\bar X$ < 74.8) = P( $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{74.8-74}{\frac{16}{\sqrt{218} } }$ ) = P(Z < 0.74) = 0.77035

The above probability is calculated by looking at the value of x = 0.74 in the z table which has an area of 0.77035.

Answer from: Quest

step-by-step explanation:

Answer from: Quest

mnkjn

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 15:40

If the slope of one line equals the slope of another line then ? a) the two lines are intersecting lines b) the two lines are perpendicular lines c) the two lines are parallel lines d) the two lines always have very steep slopes

Answers: 3

Answer

Mathematics, 21.06.2019 19:00

1. which of the following algebraic equations is equivalent to ? x^n = a a^n = x a^x = n x^a = n 2. 16^1/4= 1/2 2 4 3. (-36)^1/2= -6 1/6 no real number 4. 8^2/3= 4 8 16√2 )^5/2= 7,776 1/7,776 no real number 6. m ^ the square root of a^2m simplified is: 7. the square root of 3^3 times the square root of 2 simplified and in radical form is:

Answers: 2

Answer

Mathematics, 22.06.2019 00:30

Julie begins counting backwards from 1000 by 2’s and at the same time tony begins counting forward from 100 by 3’s. if they count at the same rate, what number will they say at the same time?

Answers: 1

Answer

Mathematics, 22.06.2019 01:30

Pls what is the decimal equivalent of 5 over 9? select one: a. 0 point 5 bar over top of 5 b. 0 point 6 bar over top of 6 c. 0 point 8 bar over top of 8 d. 0 point 9 bar over top of 9

Answers: 1

Answer

You know the right answer?

The mean of a population is 74 and the standard deviation is 16. The shape of the population is unkn...

Questions