Answer:
Carl's ACT grade had a higher z-score, which means that he earned a better score with respect to his peers on the ACT test.
Step-by-step explanation:
Z-score
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.
On which exam did Carl earn a better score with respect to his peers?
On whichever exam he had the higher z-score.
SAT
Scored 730, mean 516, standard deviation 116. So
ACT
Scored 32, mean 21, standard deviation 5.3. So
Carl's ACT grade had a higher z-score, which means that he earned a better score with respect to his peers on the ACT test.
Roper is not using a simple random sample. The samples are calculated to get 500 males and 500 females. This would be very unlikely or improbable to take place in a simple random sample. The design that they are using is a stratified sampling (dividing the population into groups) with 2 strata and these are the males and females.
Listed price = $1.4 million
Down payment = 20% of $1.4 million = 0.2 x 1,400,000 = 280,000
Amount left to pay = $1.4 million - 280,000 = $1,120,000
Present value of an annuity is given by PV = P(1 - (1 + r/t)^-nt) / r
where: PV = $1,120,000
r = 5% = 0.05
t = 12
n = 30 years.
1,120,000 = P(1 - (1 + 0.05/12)^-(12 x 30)) / 0.05
1,120,000 x 0.05 = P(1 - (1 + 1/240)^-360)
56,000 = P(1 - 0.2238)
P = 56,000 / 0.7761 = 72,148.83
Therefore, the monthly payment is $72,148.83
Answer:
80.67 hours
Step-by-step explanation:
Data provided in the question:
The number of weekly hours worked :
78 85 82 79 77 82 81 82 81 81 82 78
total number of observations = 12
Now,
Mean = (Sum of all the data values) ÷ (Total number of data values)
or
Mean = ( 78 + 85 + 82 + 79 + 77 + 82 + 81 + 82 + 81 + 81 + 82 + 78 ) ÷ 12
or
Mean = 968 ÷ 12
or Mean = 80.67 hours
Answer:
amount of pepper required= 7.5 tsp
amount of garlic powder required = 30 tsp
Step-by-step explanation:
Given,
amount of salt used for small batch of the recipe = 2 tsp
amount of pepper used for small batch of the recipe = 1 tsp
amount of garlic powder used for small batch of the recipe = 4 tsp
amount of salt used for the larger batch = 15 tsp
= 2 x 7.5 tsp
= amount of salt used for small batch the recipe x 7.5
So,
the amount of pepper needed for the larger batch= 7.5 x amount of pepper used for the small batch of recipe
= 7.5 x 1 tsp
= 7.5 tsp
the amount of garlic powder needed for the larger batch= 7.5 x amount of garlic powder used for the small batch of recipe
= 7.5 x 4 tsp
= 30 tsp
