The shape of the distribution of the time required to get an oil change at a 15 minute facility is unknown. however, records indicate that the mean time is 16.1 minutes and the standard deviation is 4.6 minutes.

a) to compute the probabilities regarding the sample mean using the normal model, what size sample would be required?

b) what is the probability that a random sample of n = 40 oil changes results in a sample mean time of less than 15 minutes?

a) choose the required sample size:

1. the normal model cannot be used if the shape is unknown

2. sample size need to be greater than 30

3. sample size needs to be less than 30

4. any sample size could be used.

b) the probability is approximately? (round to 4 decimal places as needed)

a) According to the central limit theorem the sampling distribution follows normal distribution if the size of the sample is large enough. X> or equal to 30.

Therefore the answer to the question is option 2. (Sample size need to be greater than 30)

Step-by-step explanation:

b) sample mean is 15, population mean is 16.1 , standard deviation is 3.7 and sample size is n=40

P[ z<( xbar -meu)/(sigma/sqrt(n))]

P[ z<( 15-16.1)/(3.7/√40)]

P[z< -1.1/0.5859]

P[z<-1.8803]

Checking through the standard normal distribution table

The probability to 4 d.p is 0.0300.

Also see attached picture for clearer calculation.

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.