How would these problems concerning probability and t values for examples be accessed?

A manufacturing rm claims that the batteries used in their electronic games will last an average of 34 hours. To maintain this average, 16 batteries are tested each month. If the computed t-value falls between -t0_025 and t0_025, the rm is satised with its claim. What conclusion should the rm draw from a sample that has a mean of i = 31.5 hours and a standard deviation of s = 5 hours? Assume the distribution of battery lives to be approximately normal. Since the computed t-value t= between - to.025 = and to.025 = , the firm should satisfied with the claim. (Round to three decimal places as needed.)\fAtaxi company tests a random sample of 10 steel-belted radial tires of a certain brand and records the tread wear in kilometers, as shown below. 48,000 42,000 49,000 69,000 67,000 63,000 64,000 43,000 53,000 41,000 D If the population from which the sample was taken has population mean u =43,000 kilometers, does the sample information here seem to support that claim? In your )1 - 43,000 six/W answer, compute t= and determine from the tables (with 9 d.f.) whether the computed t-value is reasonable or appears to be a rare event. A random sample of size 36 is taken from a normal population having a mean of 70 and a standard deviation of 2. A second random sample of size 64 is taken from a different normal population having a mean of 65 and a standard deviation of 5. Find the probability that the sample mean computed from the 36 measurements will exceed the sample mean computed from the 64 measurements by at least 3.7 but less than 5.4. Assume the difference of the means to be measured to the nearest tenth.Two different box-filling machines are used on an assembly line. The critical measurement influenced by these machines is the weight of the product in the boxes. Engineers are quite certain that the variance of the weight of product is of = 2 ounces. Experiments are conducted using both machines with sample sizes of 49 each. The sample averages for machines A and B are XA = 10.7 ounces and X = 11.0 ounces. Engineers are surprised that the two sample averages for the filling machines are so different. Complete parts (a) and (b) below.(a) Use the Central Limit Theorem to determine P()_(B - )_(A 2 0.3) under the condition that \"A = uB. P()_(B - )'(A 2 0.3) =