Use a statistics calculator to find the area, in decimal form, rounded to four places after the decimal, under the (standard) No
1 answer:
Answer:
a) 0.9641.
b) 0.0082
c) 0.0277
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
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) ...to the left of 1.8.
p-value of Z = 1.8, which, looking at the z-table, is of 0.9641.
(b) ...to the right of 2.4.
1 subtracted by the p-value of Z = 2.4.
Looking at the z-table, Z = 2.4 has a p-value of 0.9918.
1 - 0.9918 = 0.0082, which is the answer.
(c) ...between 1.8 and 2.4.
p-value of Z = 2.4 subtracted by the p-value of Z = 1.8.
From itens a and b, we have both. So
0.9918 - 0.9641 = 0.0277
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Answer:
The p-value is less than the significance level, so we will reject the null hypothesis, and conclude that at 5% significance level, the proportion for women that ran 5 km is more than the proportion of male that ran the 5 km. Thus, women are more likely to run the 5 km race.
Step-by-step explanation:
We are given;
Number of males selected; n₁ = 150
Number of females selected; n₂ = 190
Proportion of the males; p₁ = 0.6
Proportion of females; p₂ = 0.5
Let's define the hypotheses;
Null hypothesis; H0: p₁ ≥ p₂
Alternative hypothesis; Ha: p₁ < p₂
Now, the z score formula for this is;
z = (p₁ - p₂)/√(p^(1 - p^))(1/n₁ + 1/n₂))
Where;
p^ = (p₁ + p₂)/2
p^ = (0.6 + 0.5)/2
p^ = 0.55
Thus;
z = (0.6 - 0.5)/√(0.55(1 - 0.55))((1/150) + (1/190))
z = 0.1/0.0543
z = 1.84
From online p-value from z-score calculator attached, using z = 1.84, significance level = 0.05, one tailed hypothesis, we have;
P-value = 0.033
The p-value is less than the significance level, so we will reject the null hypothesis, and conclude that at 5% significance level, the proportion for women that ran 5 km is more than the proportion of male that ran the 5 km. Thus, women are more likely to run the 5 km race.
Although if we check at 0.01 significance level, we will not have the same answer as the p-value will be greater.
notice the first term is -10, and the common difference is 3, so we add 3 to get the next term.
check the picture below.
