Answer:
0.7673
Step-by-step explanation:
in this question, we are asked to calculate a probability.
firstly. we start by calculating the z score, then onwards, we check the normal distribution table.
please check attachment for full and complete answer
Answer:
P  (  x_sample mean  <  20948 ) = 0.7673
Step-by-step explanation:
Given:-
- The mean, u = 20,908
- Standard deviation,  σ  =  407
- Sample size,  n  =  55.
Find:-
The required probability is  P  (  x_sample mean  <  20948 )
Solution:-
In this question, the probability of the sample mean is calculated by the z-test statistic under the normal probability. The z-test statistic is a normal test statistic and it is used for a large sample size in a normal probability problem.
- Determine the Z-score value for the statistics:
       P  (  x_sample mean  <  20948 ) = P ( Z < (x - u )*√n / σ )
                               = P ( Z < (20,948 - 20,908 )*√55 / 407)
                               = P ( Z < 0.73)
- Using the Z-Table we determine the probability for P ( Z < .73 ):
       P ( Z < 0.73 ) = 0.7673
       P  (  x_sample mean  <  20948 ) = 0.7673
