Note: Hello, for this question I need all of the answerswith and explanation and obviously with the work andanswer, The formulas for this question are1) CLT : Central limit theorem2) Also depending what is the question asking here arethe formulas that I can use, please do not use any otherformulas1)Temperatures in a certain part of the world are normally distributed with mean 24 and standard deviation 6, when checked at noon each day.A) Draw a graph of this distributionB) What temperature Correspondsto One standard deviation above the mean?c)What is the probability that the temperatureis above the answer that you gave in part (b)d)What is the probability, that the temperaturebetween 21and 32 ? E)How many days of the year have their temperature between 21 and 32,when checked at noon?2) Using the mean and standard deviation from question 1), what temperature Corresponds to theColdest 20% of all days?(Find the temperature that cuts off the bottom 20%of the distribution).3. A tire manufacturer claims that the useful life of its tires is normally distributed with M= 35,000 miles and Standard deviation = 5,000 miles.a)If one tire is selected at randomlasts 31,000 miles, convertthis number to a z-score.b)If a sample of 90 tires is considered and their mean life, X, is 31,000 miles, Convert this number toe Z-scorec) Why are these answer hegative?d)Why are your two answers different from each other?4) At a particular restaurant the mean timefor a customer to wait for a table is 16.3 minutes with standard deviation 5.8 minutes. (Assume normal distribution.)A) If a customer is selected, what is the probability that their Wait time is less than 18 minutes?B) What is the probability that their wait time is morethan 45 minutes?5) In raw milk, a certain strain of bacteric should occur with mean= 2500 bacterias per millilitor with standard deviation =300. A) If a health inspector takes 42 random samples of milk What is the probability that the average count,for those Samples is between 2400 and 2600bacteria per militer? B) why can we use the CLT for this question ? 6) It has been found that 80% of all productsintroduced in a grocery store fail within 2 years (are taken off the market) If a certain grocery storeintroduces 66 new products,What is the probabilitythat 56 or fewer will fail in the first two years?

Important Formulas Formula for the z score (or standard score): X - H Z = Formula for finding a specific data value: X =z ' 6+ H Formula for the mean of the sample means: HX-H Formula for the standard error of the mean: X - H Z = 6/ Vn Formula for the z value for the central limit theorem: Vn Formulas for the mean and standard deviation for the binomial distribution: H =n . p 6 = Vn .p