Petra jogs 3 miles in 30 minutes. At this rate, how long would it take her to jog 7 miles?
1 answer:
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7 more year 9 students than year 8 students should be surveyed, If Mr.Ford wants to survey 50 of these students stratified by year group.
Step-by-step explanation:
The given is,
Year Students
7 80
8 110
9 160
Total 350
Mr.Ford wants to survey 50 of these students stratified by year group.
Step:1
Formula to find the ratio of number of grouped students to total students,
=
= 0.1428
Step:2
Formula for Number of students surveyed from year wise,
For year 7 students,
= (Ratio) × (Students from year 7)
= 0.1428 × 80
= 11.424
≅ 11 (∵ For students we convert into whole number)
For year 8 students,
= (Ratio) × (Students from year 8 )
= 0.1428 × 110
= 15.708
≅ 16 (∵ For students we convert into whole number)
For year 8 students,
= (Ratio) × (Students from year 9 )
= 0.1428 × 160
= 22.8
≅ 23 (∵ For students we convert into whole number)
Step:3
To find How many more year 9 students than year 8 students should be in the survey
= ( Students from year 8 for group) -
( Students from year 8 for group)
= 23 - 16
= 7 students
Result:
7 more year 9 students than year 8 students should be surveyed, If Mr.Ford wants to survey 50 of these students stratified by year group.
Answer:
The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of , in which
is mean amount of inches of rain and
is the standard deviation.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
Mean , standard deviation
n days:
This means that
Applying the Central Limit Theorem to the z-score formula.
What is the probability that the mean daily precipitation will be of X inches or less for a random sample of November days?
The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of , in which
is mean amount of inches of rain and
is the standard deviation.