Need help Q6 andarcO BinomialTn Unit 4 Te xE RoundinA scde genR.mroons.ne/mod/quiz/attempt.php?...Empirical RuleUse the Empirical Rule to find the following probabilities. It is suggested thatyou draw a normal curve, label the x-values for 1, 2, and 3 standard deviationsfrom the mean, and write in the probabilities between each standard deviationbefore attempting to answer the questions.The average life-span of a True Test auto battery is 39 months with a standarddeviation of 3 months. Assume a normal distribution.1. We can expect 95% of the batteries to last betweenandmonths.2. We can expect%.of the batteries to last less than 30months.3. We can expect% of the batteries to last longer than 42months.4. We can expect% of the batteries to last between 30 and39 months.5. We can expect% of the batteries to last between 42 and48 months.3:02 PM12/9/2020II

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Description: Need help Q6 andarcO BinomialTn Unit 4 Te xE RoundinA scde genR.mroons.ne/mod/quiz/attempt.php?...Empirical RuleUse the Empirical Rule to find the following probabilities. It is suggested thatyou draw a normal curve, label the x-values for 1, 2, and

Note: Hey, since multiple subparts are posted, we will answer first three subparts according to our policy. If you want any specific subpart to be answered, then please submit that subparts only in your message.68-95-99.7-rule: Let X be an observation from a normal distribution, having mean µ and standard deviation σ, then according to the 68-95-99.7-rule, approximately 68%,95% and 99.7% of the values lie within one, two and three standard deviations of the mean respectively. That is, Pμ-1σ≤X≤μ+1σ≈0.68Pμ-2σ≤X≤μ+2σ≈0.95Pμ-3σ≤X≤μ+3σ≈0.997Here, µ =39 and σ = 3. The 1, 2, and 3 sigma limits are as follows: μ±1σ=39±1×3=36,42μ±2σ=39±2×3=33,45μ±3σ=39±3×3=30,481) We can expect 95% of the observations within 2 standard deviations of mean. We can expect 95% of the batteries last between 33 and 45. 2) It is known that 99.7% of the data lies within three standard deviations of the mean. 99.7% of data lies between 30 and 48. There is only 0.3% of the area outside the 3 sigma limit. The probability that an observation is less than 30 is 0.15% (=0.3/2). We can expect 0.15% of the batteries to last less than 30 months. 3) It is known that 68% of the data lies within one standard deviations of the mean. 68% of data is between 36 and 42. Since normal distribution is symmetric about mean, 34% (=68/2) of the observations are lies between 39 and 42. Since the normal distribution is symmetric about mean, about 50% of the data are above 39. Thus, the probability that a battery last longer than 42 is 50%-34% =16%. We can expect 16% of the batteries to last longer than 42 months.