Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Answer:
a) P(Z > 1.09) = 0.1379
b) P(Z < -0.22) = 0.4129.
c) P(Z < -1.96) = 0.025, P(Z > -1.96) = 0.025
d) Z = 1.4
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
a. P(Z > 1.09)
This is 1 subtracted by the pvalue of Z = 1.09.
Z = 1.09 has a pvalue of 0.8621
1 - 0.8621 = 0.1379, so
P(Z > 1.09) = 0.1379
b. P(Z < -0.22)
This is the pvalue of Z = -0.22.
Z = -0.22 has a pvalue of 0.4129. So
P(Z < -0.22) = 0.4129.
c) P(Z < -1.96) or P(Z > -1.96)
Z = -1.96 has a pvalue of 0.025. So
1 - 0.025 = 0.975
P(Z < -1.96) = 0.025
P(Z > -1.96) = 0.025
d. What is the value of Z if only 8.08% of all possible Z-values are larger?
Z with a pvalue of 100 - 8.08 = 91.92 = 0.9192, so Z = 1.4
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.