Q SCI 381
Dr.Bare
Name:________________________
Hourly Examination Three Answers
1.a. Use the z-distribution to find the z-values corresponding to the two
given x-values. You should find that 82 bushels corresponds to a z-value
of -1.75 and 138 bushels corresponds to z = 1.75. From the z-table, the
area under the z-curve between these two values = 0.9198.
1.b. Find the z-value with .0500 area to its left in the z-table to be
-1.645. Similarly, the z-value with .9500 area to its left is found in the
z-table to be 1.645. Using the formula from p. 254 of your text, you
transform the z-score to the x-scale and obtain the two x-values of 83.68
and 136.32.
2.a. The max error of estimate is: 4.262. (Here we use the t-table.)
2.b. The 95% C.I. is 120 +(-) 4.262
2.c. We are 95% confident the interval 120 +(-) 4.262 contains the true
(unknown) mean blood pressure.
3. Use the definition of the z-variable described in Sec 5.4 and find z = 5.728. From
the z-table, the probability that a sample mean is greater than 5.728
standard deviations is about 0.
4.a. Review p. 309 where the finite population correction factor
is defined. If n >= 0.05N and sampling is done w/o replacement, then the correction is
warranted. Here we have
49 >= 30 so it is needed.
4.b. z-distribution as n>= 30
4.c. E = 1.645 (1.37) = 2.25 and the 90% C.I. = 125 +(-) 2.25
4.d. We are 90% confident that the interval 125 +(-) 2.25 contains the
true mean IQ of statistic instructors.
5. Use procedure from p. 332 and chi-square table 6. The appropriate
chi-square values from the table are chi-square left = 6.571 and
chi-square right = 23.685. The 90% C.I. for the variance is: 21.28 - 76.70 and upon
taking the square root, the C.I. for the standard deviation is: 4.61-8.76.
6. Yes, we meet the two conditions for using the normal approximation of
the binomial. Both np and nq >= 5. The appropriate z-value calculated
using the formula from p. 278 is 1.99. From the z-table, the probability of
30 or more streams containing fish is 1 - .9767 = .0233
7. Use formula from p. 304. n = 43.3 or 44 crows.