1.Let X be a standard normal random variable. Find P(X < 0). Express your answer as a decimal.2.Let X be a standard normal random variable. Find P(X ≤ -2.27). Express your answer as a decimal.3.Let X be a standard normal random variable. Find P(X > 2.82). Express your answer as a decimal.4.Let X be a standard normal random variable. Find P(-1.20 < X < 1.74). Express your answer as a decimal.5.Assume that thermometer readings are normally distributed with a mean of 0 degrees Celsius and a standard deviation of 1 degree Celsius. A thermometer is randomly selected and tested. Find the temperature reading that separates the bottom 95% from the top 5%. Round your answer to the nearest thousandth6.Assume that thermometer readings are normally distributed with a mean of 0 degrees Celsius and a standard deviation of 1 degree Celsius. A thermometer is randomly selected and tested. Find the temperature reading that separates the bottom 40.9% from the top 59.1%. Round your answer to the nearest hundredth.

Assignment: Note: This Assignment consists of two parts. You will complete and submit Part 1 this week, and you will complete and submit Part 2 next week.Companies often develop and test hypotheses about their products. For example, car manufacturers will test their cars to determine fuel efficiency and miles per gallon. To ensure that products are safe and that they perform as advertised, regulatory and consumer protection groups also test companies’ claims.For this Assignment, you are working at a firm that conducts independent testing for heavy industry. Recently, an automobile manufacturer has been in the news for complaints about the highway gas mileage of their latest model minivan. You receive a contract from a consumer action group to test and write a report on the company’s claim that its minivans get 28 miles per gallon on the highway. The car company agrees to allow you to select randomly 35 low-mileage fleet minivans to test their highway mileage. Your test results gave you the following data: 29.7 24.5 27.1 29.8 29.2 27.0 27.8 24.1 29.3 25.9 26.2 24.5 32.8 26.8 27.8 24.0 23.6 29.2 26.5 27.7 27.1 23.7 24.1 27.2 25.9 26.7 27.8 27.3 27.6 22.8 25.3 26.6 26.4 27.1 26.1To prepare for this Assignment:Refer to the scenario above and the data that was provided by the car company (please see above)Submit Part 1 of your report according to the following prompts.Part 1: Sample Mean, Standard Deviation, and Confidence IntervalComplete the following and include your results and responses in your report:Include a brief introduction that provides a context for the assignment you have been given by your firm.Calculate a 95% confidence interval around your sample mean. (75 words, or 1 paragraph)Note: Include your calculations. If your calculations are submitted separately, make note of where they can be found.Is the company’s claimed mean inside your confidence interval? (75 words, or 1 paragraph)What does that result indicate about the company’s claim? (75 words, or 1 paragraph)3 prompts: 1 citation for each prompt. APA style, Times new roman 12, double space.