Answer:
Option E.
Step-by-step explanation:
Let the intended length of Rebecca's swimming is = x units
and we assume the length of the pool = l units
Now it is given in the question that " She covers one fifth of her intended distance "
That means distance covered =
" After swimming six more lengths of the pool she had covered one quarter of her intended distance"
So
x = 20×(6l)
x = 120l
Therefore, Rebecca has to complete 120 lengths of the pool.
Option E is the answer.
Answer:
a) 0.0853
b) 0.0000
Step-by-step explanation:
Parameters given stated that;
H₀ : <em>p = </em>0.6
H₁ : <em>p = </em>0.6, this explains the acceptance region as;
p° ≤ =0.63 and the region region as p°>0.63 (where p° is known as the sample proportion)
a).
the probability of type I error if exactly 60% is calculated as :
∝ = P (Reject H₀ | H₀ is true)
= P (p°>0.63 | p=0.6)
where p° is represented as <em>pI</em><em> </em>in the subsequent calculated steps below
= P
= P
= P
= P [Z > 1.37]
= 1 - P [Z ≤ 1.37]
= 1 - Ф (1.37)
= 1 - 0.914657 ( from Cumulative Standard Normal Distribution Table)
≅ 0.0853
b)
The probability of Type II error β is stated as:
β = P (Accept H₀ | H₁ is true)
= P [p° ≤ 0.63 | p = 0.75]
where p° is represented as <em>pI</em><em> </em>in the subsequent calculated steps below
= P
= P
= P
= P [Z ≤ -6.20]
= Ф (-6.20)
≅ 0.0000 (from Cumulative Standard Normal Distribution Table).