Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
Using the normal distribution, there is a 0.3228 = 32.28% probability that at least 90 cars pass inspection.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
- The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].
The parameters for the binomial distribution are given by:
n = 100, p = 0.88.
Hence the mean and the standard deviation for the approximation are:
- [tex]\mu = np = 100 \times 0.88 = 88[/tex]
- [tex]\sigma = \sqrt{np(1-p)} = \sqrt{100 \times 0.88 \times 0.12} = 3.25[/tex]
The probability that at least 90 cars pass inspection, using continuity correction, is P(X > 89.5), which is one subtracted by the p-value of Z when X = 89.5, hence:
Z = (89.5 - 88)/3.25
Z = 0.46
Z = 0.46 has a p-value of 0.6772.
1 - 0.6772 = 0.3228.
0.3228 = 32.28% probability that at least 90 cars pass inspection.
More can be learned about the normal distribution at https://brainly.com/question/15181104
#SPJ1
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.
