90<-30p+15 how do you solve this
1 answer:
<em>*To solve an inequality, it's the same as if you were solving an equation: Isolate the desired variable to one side to solve.</em>
Firstly, subtract 15 on both sides:
Next, you are going to divide both sides by -30. Since you are dividing by a <u>negative,</u> you are going to flip the inequality symbol. <u>Your final answer will be: </u>
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Answer:
0.4010 = 40.10% probability that the sample mean would differ from the population mean by more than 0.8 millimeters
Step-by-step explanation:
To solve this question, we need to understan the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
Either the sample mean differs by 0.8 mm or less from the population mean, or it differs by more. The sum of these probabilities is decimal 1.
Probability it differs by less than 0.8mm
pvalue of Z when X = 139 + 0.8 = 139.8mm subtracted by the pvalue of Z when X = 139 - 0.8 = 138.2 mm
X = 139.8
By the Central Limit Theorem
has a pvalue of 0.7995
X = 138.2
has a pvalue of 0.2005
0.7995 - 0.2005 = 0.5990
What is the probability that the sample mean would differ from the population mean by more than 0.8 millimeters?
p + 0.5990 = 0.4010
0.4010 = 40.10% probability that the sample mean would differ from the population mean by more than 0.8 millimeters
Answer:
The savings of Sid and Tim will be in 17:9 in 6 weeks.
Step-by-step explanation:
Initial savings of Sid = £ 13
Initial savings of Tim = £ 0
For each successive week Sid saved = £ 3.5
For each successive week Tim saved = £ 3
Let us assume that after "x weeks" the amounts of Sid and Tim are in ratio 17:9.
If Sid saves £ 3.5 in one week, in x weeks he will £ 3.5x. Since he had £ 13 initially, total amount he would have in x weeks will be £ (13 + 3.5x)
If Time saves £ 3 one week, in x weeks he will save £ 3x. Since, he didn't have any money initially, in x weeks he would have saved £ 3x
The ratio of their savings in x weeks would be 17:9
So,
Sid's saving : Tim's saving = 17 : 9
Using the values of expressions, we get:
This means, the savings of Sid and Tim will be in 17:9 in 6 weeks.