Mathematics, 17.06.2021 17:10 infoneetusinghoyg22o

Suppose that past records indicate that the probability that a new car will need a warranty repair in the first 90 days of use is 0.04. If a random sample of 400 new cars is selected. what is the probability that the proportion of new cars needing a warranty repair in the first 90 days will be: a. between 0.05 and 0.06? i. e. P(0.05 SpS 0.06) = (round your answer to 4 decimal places). b. above 0.07? i. e. P(p > 0.07) = (round your answer to 5 decimal places) c. below 0.03?ie. P(p < 0.03) = (round your answer to 4 decimal places)

Answers: 3

Show answers

Answers

Answer from: sandrathompson7250

a) P(0.05 < p < 0.06) = 0.1332

b) P(p > 0.07) = 0.0011.

c) P(p < 0.03) = 0.1539

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Suppose that past records indicate that the probability that a new car will need a warranty repair in the first 90 days of use is 0.04.

This means that p = 0.04

Sample of 400.

This means that $n = 400, s = \sqrt{\frac{0.04*0.96}{400}} = 0.0098$

a. between 0.05 and 0.06?

This is the p-value of Z when X = 0.05 subtracted by the p-value of Z when X = 0.05. So

X = 0.06

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{0.06 - 0.04}{0.0098}$

Z = 2.04

Z = 2.04 has a p-value of 0.9793.

X = 0.05

$Z = \frac{X - \mu}{s}$

$Z = \frac{0.05 - 0.04}{0.0098}$

Z = 1.02

Z = 1.02 has a p-value of 0.8461.

0.9793 - 0.8461 = 0.1332

P(0.05 < p < 0.06) = 0.1332

b. above 0.07?

This is 1 subtracted by the p-value of Z when X = 0.07. So

$Z = \frac{X - \mu}{s}$

$Z = \frac{0.07 - 0.04}{0.0098}$

Z = 3.06

Z = 3.06 has a p-value of 0.9989.

1 - 0.9989 = 0.0011. So

P(p > 0.07) = 0.0011.

c. below 0.03?

This is the p-value of Z when X = 0.03. So

$Z = \frac{X - \mu}{s}$

$Z = \frac{0.03 - 0.04}{0.0098}$

Z = -1.02

Z = -1.02 has a p-value of 0.1539. So

P(p < 0.03) = 0.1539

Answer from: Quest

idk

step-by-step explanation:

Answer from: Quest

answer download the app called socratic on your phoner:

step-by-step explanation:

What is the most likely reason bismarck was named chancellor when king wilhelm i became kaiser of ge

Another question on Mathematics

Mathematics, 21.06.2019 18:00

The swimming pool is open when the high temperature is higher than 20∘c. lainey tried to swim on monday and thursday (which was 3 days later). the pool was open on monday, but it was closed on thursday. the high temperature was 30∘c on monday, but decreased at a constant rate in the next 3 days. write an inequality to determine the rate of temperature decrease in degrees celsius per day, d, from monday to thursday.

Answers: 1

Answer

Mathematics, 21.06.2019 18:30

How do you solving the solution of each system using elimination?

Answers: 2

Answer

Mathematics, 21.06.2019 20:30

If a 36 inch yardstick casts a 21 foot shadow, how tall is a building whose shadow is 168 feet? what is the scale factor

Answers: 1

Answer

Mathematics, 21.06.2019 21:30

Consider a bag that contains 220 coins of which 6 are rare indian pennies. for the given pair of events a and b, complete parts (a) and (b) below. a: when one of the 220 coins is randomly selected, it is one of the 6 indian pennies. b: when another one of the 220 coins is randomly selected (with replacement), it is also one of the 6 indian pennies. a. determine whether events a and b are independent or dependent. b. find p(a and b), the probability that events a and b both occur.

Answers: 2

Answer

You know the right answer?

Suppose that past records indicate that the probability that a new car will need a warranty repair i...

Questions