Question 1 The average math SAT score is 511with a standard deviation of 119. A particular…

Question 1
The average math SAT score is 511with a standard deviation of
119. A particular high school claims that its students have
unusually high math SAT scores. A random sample of 50 students from
this school was​ selected, and the mean math SAT score was 555. Is
the high school justified in its​ claim? Explain.
▼ Pick one
No
Yes
​because the​ z-score (what is the z score)
​(?​)
is
▼ pick one
not unusual
unusual
since it
▼ pick one
lies
does not lie
within the range of a usual​ event, namely
within
▼ pick one
1 standard deviation
2 standard deviations
3 standard deviations
of the mean of the sample means
Question 2
The lengths of lumber a machine cuts are normally distributed
with a mean of 102 inches and a standard deviation of 0.4 inch.
​(a) What is the probability that a randomly selected board cut
by the machine has a length greater than 102.11 ​inches?
​(b) A sample of 43 boards is randomly selected. What is the
probability that their mean length is greater than 102.11
inches?
Question 3:
The weights of ice cream cartons are normally distributed with a
mean weight of 9 ounces and a standard deviation of 0.4 ounce.
​(a) What is the probability that a randomly selected carton has
a weight greater than 9.13 ounces?
​(b) A sample of 36 cartons is randomly selected. What is the
probability that their mean weight is greater than 9.13 ounces?