Step-by-step explanation:
a.
mean = 266
sd = 14
cumulative probability = 0.01 so the standard score = -2.33 and 2.33 to the right and left
we find X-upper and X-lower
X-lower = 266-2.33*14 = 233.38
X-upper = 266+2.33*14 = 298.62
Between 233.38 and 298.62
we have sample size = 35
X-lower = 266-2.33*14/√35 = 260.49
X-upper = 266+2.33*14/√35 = 271.5
Between 260.49 and 271.5
b. cumulative probaility = 0.25
standard score = 1.96 to the right and left
x-lower = 6.9-1.96x0.9 = 5.14
x-upper = 6.9+1.96x0.9 = 8.66
Between 5.14 and 8.66
if sample size = 45
x-lower = 6.9-1.96*0.9/√45 = 6.64
x-upper = 6.9+1.96*0.9/√45 = 7.2
Between 6.64 and 7.2
c. standard scores would have cut off value at 0.67 and -0,67
x-lower = 265.3-0.67x15.2 = 255.12
x-upper = 265.3+0.67x15.2 = 275.48
Between 255.12 and 275.48
d. we will have critical values at 1.00 and -1.00
X-lower = 265-1x16 = 249
x-upper = 265+1x16 = 281
Between 249 and 281
with sample size = 44
x-lower = 265-1x16/√44 = 262.59
x-upper = 265+1x16/√44 = 267.41
Between 262.59 and 267.41
