Using the normal distribution, it is found that:
a) 0.8599 = 85.99% probability that x is more than 60.
b) 0.1788 = 17.88% probability that x is less than 110.
c) 0.6811 = 68.11% probability that x is between 60 and 110.
d) 0.0643 = 6.43% probability that x is greater than 125.
In a normal distribution with mean and standard deviation
, the z-score of a measure X is given by:
In this problem:
Item a:
This probability is <u>1 subtracted by the p-value of Z when X = 60</u>, thus:
has a p-value of 0.1401.
1 - 0.1401 = 0.8599
0.8599 = 85.99% probability that x is more than 60.
Item b:
This probability is the <u>p-value of Z when X = 110</u>, thus:
has a p-value of 0.8212.
1 - 0.8212 = 0.1788.
0.1788 = 17.88% probability that x is less than 110.
Item c:
This probability is the <u>p-value of Z when X = 110 subtracted by the p-value of Z when X = 60</u>.
From the previous two items, 0.8212 - 0.1401 = 0.6811.
0.6811 = 68.11% probability that x is between 60 and 110.
Item d:
This probability is <u>1 subtracted by the p-value of Z when X = 125</u>, thus:
has a p-value of 0.9357.
1 - 0.9357 = 0.0643.
0.0643 = 6.43% probability that x is greater than 125.
A similar problem is given at brainly.com/question/24863330