Answer:
45 degree
Step-by-step explanation:
We are given that
Angle PSR=99 degrees
Angle PSQ=(3x+18) degrees
Angle QSR=(9x-27)degrees
According to question
Angle PSR=Angle PSQ+angle QSR
Substitute the values
Substitute the value of x
Angle PSQ=
Hence, the measure of angle PSQ=45 degree
Answer:
a) 0.997 is the probability that the breaking strength is at least 772 newtons.
b) 0.974 is the probability that this material has a breaking strength of at least 772 but not more than 820
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 800 newtons
Standard Deviation, σ = 10 newtons
We are given that the distribution of breaking strength is a bell shaped distribution that is a normal distribution.
Formula:
a) P( breaking strength of at least 772 newtons)
Calculation the value from standard normal z table, we have,
0.997 is the probability that the breaking strength is at least 772 newtons.
b) P( breaking strength of at least 772 but not more than 820)
0.974 is the probability that this material has a breaking strength of at least 772 but not more than 820.
Answer:
a) Failed to reject the null hypothesis (P-value=0.09).
b) The 95% CI for the difference in proportions is:
Step-by-step explanation:
a) We have to perform a hypothesis test for the difference of proportions.
The null and alternative hypothesis are:
The significance level is 0.05.
The proportion of the passenger cars owners is:
The proportion of commercial truck owners is:
The weigthed average p is
The estimated standard deviation is
We can calculate the z-value as:
The P-value for z=-1.362 is P=0.0866.
The P-value (0.09) is greater than the significance level (0.05), so it failed to reject the null hypothesis. There is no enough evidence to prove that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars.
b) We can construct a 95% CI, according to the significance level of 0.05.
The z-value for this CI is 1.96.
We have to recalculate the standard deviation:
The lower limit is then:
The upper limit is:
The 95% CI for the difference in proportions is:
In this case, we can conclude that the difference between the proportions, with 95% confidence, can still be equal or greater than zero, meaning that it is possible passenger car owners violate laws more than truck owners.