To test μ for an x distribution that is mound-shaped using sample size n ≥ 30, how do you decide whether to use the normal or student's t distribution?

a. if σ is known, use the standard normal distribution. if σ is unknown, use the student's t distribution with n – 1 degrees of freedom.
b. if σ is unknown, use the standard normal distribution. if σ is known, use the student's t distribution with n – 1 degrees of freedom.
c. if σ is known, use the standard normal distribution. if σ is unknown, use the student's t distribution with n degrees of freedom.
d. for large samples we always the standard normal distribution.

The correct option is A) If σ is known, use the standard normal distribution. If σ is unknown, use the Student's t distribution with n – 1 degrees of freedom.

Step-by-step explanation:

Consider the provided information.

The t-distribution of the Student is a distribution of probability that is used when when the sample size is small and/or when the population variance is unknown to estimate population parameters.

The number of independent observations is equal to the sample size minus one when calculating a mean score or a proportion from a single sample.

Since µ and σ determine the shape of the distribution so we use standard normal distribution if σ is known.

Hence, the correct option is A) If σ is known, use the standard normal distribution. If σ is unknown, use the Student's t distribution with n – 1 degrees of freedom.

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step-by-step explanation:

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)