Question

Select all statements that are true for density curves.

(A) The total area under the curve is 1.

(B)The curve satisfies the 68-95-99.7% rule.

(C)The curve is on or above the horizontal axis.

(D)The curve is symmetric and single-peaked.

(E)The proportion of data values between two numbers aa and bb is the area under the curve between aa and bb.

Answer 1

statement (A) is correct as it is the property of density function.

statement (C) is also correct as the density function is always above the horizontal line or have positive values.

statement (E) is also true as the proportion of data values between two points aa and bb represent the relative frequency of all observation that lie between that points is represented as area under that region.

statement (D) is false because a density function is not always symmetric, it also has different shapes and peaks.

statement (B) the 68-95-99.7 rule,also known as empirical rule is a shorthand used to remember the percentage of values that lie within a band around the mean value of a normal density curve.