Question

A random sample of size n = 50 is taken from a population with mean μ = −9.5 and standard deviation σ = 2. [You may find it useful to reference the z table.]

a. Calculate the expected value and the standard error for the sampling distribution of the sample mean. (Negative values should be indicated by a minus sign. Round "expected value" to 1 decimal place and "standard deviation" to 4 decimal places.)

Expected Value=

Standard Error=

b. What is the probability that the sample mean is less than −10? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

Probility=

c. What is the probability that the sample mean falls between −10 and −9? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

Probility=

***Please write ans clearly

Answer 1

Solution :

Given that,

mean = = -9.5

standard deviation = = 2

a.

n = 50

= -9.5

= / n = 2 / 50 = 0.2828

b.

P( < -10) = P(( - ) / < (-10 - (-9.5)) / 0.2828)

= P(z < -1.77)

= 0.0384

Probability = 0.0384

c.

= P[(-10 - (-9.5)) / 0.2828 < ( - ) / < (-9 - (-9.5)) / 0.2828)]

= P(-1.77 < Z < 1.77)

= P(Z < 1.77) - P(Z < -1.77)

= 0.9616 - 0.0384

= 0.9232

Probability = 0.9232