Find z such that 87.7% of the standard normal curve lies to the left of z. (round your answer to two decimal places.)

z=

assume that x has a normal distribution with the specified mean and standard deviation. find the indicated probability. (round your answer to four decimal places.)

μ = 2.4; σ = 0.35

p(x ≥ 2) =

find z such that 6% of the standard normal curve lies to the right of z. (round your answer to two decimal places.)

z =

a) z = 1.16

b) P(x ≥ 2) = 0.8508

c) z = 1.555

Step-by-step explanation:

a) Find z such that 87.7% of the standard normal curve lies to the left of z.

Lies to the left, so it has a pvalue of 0.877. This is z = 1.16

b) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability.

μ = 2.4; σ = 0.35

P(x ≥ 2) =

This is 1 subtracted by the pvalue of Z when X = 2, in which

has a pvalue of 0.1492.

So

P(x ≥ 2) = 1 - 0.1492 = 0.8508.

c) Find z such that 6% of the standard normal curve lies to the right of z.

To the right, so z has a pvalue of 1-0.06 = 0.94%. So z = 1.555.

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.