Suppose a simple random sample of size nequals1000 is obtained from a population whose size is Nequals1 comma 000 comma 000 and whose population proportion with a specified characteristic is p equals 0.47 . Complete parts (a) through (c) below. (a) Describe the sampling distribution of ModifyingAbove p with caret.
A.
Approximately normal, mu Subscript ModifyingAbove p with caretequals0.47 and sigma Subscript ModifyingAbove p with caretalmost equals0.0002
B.
Approximately normal, mu Subscript ModifyingAbove p with caretequals0.47 and sigma Subscript ModifyingAbove p with caretalmost equals0.0158
C.
Approximately normal, mu Subscript ModifyingAbove p with caretequals0.47 and sigma Subscript ModifyingAbove p with caretalmost equals0.0005
(b) What is the probability of obtaining xequals510 or more individuals with the characteristic?
P(xgreater than or equals510)equals
nothing (Round to four decimal places as needed.)
(c) What is the probability of obtaining xequals440 or fewer individuals with the characteristic?
P(less than or equals440)equals
nothing (Round to four decimal places as needed.)