35. a) If the mean of a small sample is 10, the standard deviation is 1, and the

Question

35. a) If the mean of a small sample is 10, the standard deviation is 1, and the t-value for 90% confidence is 1.761, how many measurements are there in the sample set?

A:14 ,B:15 ,C:21 ,D:25 ,E:29

b) A 2V standard deviation is found for a normally distributed set of 100 battery voltage measurements and the mean of the data is 12V. Based on the information, how many measured values might you expect to be between 10 and 14V?

A:50 ,B:57 ,C:68 ,D:74 ,E:82

I would really appreciate it if you could explain the questions via steps. Thanks.

Explanation / Answer

(a) Refrrring to the areas under the t- distribution, we find that for = 0.10 and t = 1.761, degrees of freedom = 14

So, sample size = 14 + 1 = 15

Option B

(b) n = 100, = 12, = 2

z1 = (10 - 12)/2 = -1 and z2 = (14 - 12)/2 = 1

P(10 < x < 14) = P(-1 < z < 1) = 0.6828

Number of values = 0.6827 * 100 = 68 values.

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