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drek231 [11]
3 years ago
9

Suppose the time that it takes a certain large bank to approve a home loan is Normally distributed with mean (in days) μ and sta

ndard deviation σ=1. The bank advertises that it approve loans in 5 days, on average, but measurements on a random sample of 500 loan applications to this bank gave a mean approval time of = 5.3 days. Is this evidence that the mean time to approval is actually longer than advertised? To answer this, test the hypotheses H0:μ=5, Ha:μ>5 at significance level α=0.01. You conclude that: a. Ha should be rejected.b. there is a 5% chance that the null hypothesis is true.c. H0 should be rejected.d. H0 should not be rejected.
Mathematics
1 answer:
kolezko [41]3 years ago
4 0

Answer:

(c) H0 should be rejected

Step-by-step explanation:

Null hypothesis (H0): population mean is equal to 5

Alternate hypothesis (Ha): population mean is greater than 5

Z = (sample mean - population mean) ÷ (sd/√n)

sample mean = 5.3, population mean = 5, sd = 1, n = 500

Z = (5.3 - 5) ÷ (1/√500) = 0.3 ÷ 0.045 = 6.67

Using the normal distribution table, for a one tailed test at 0.01 significance level, the critical value is 2.326

Conclusion:

Since 6.67 is greater than 2.326, reject the null hypothesis (H0)

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maxonik [38]

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5 0
3 years ago
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You place $4,000.00 in a bank account with an interest rate of 5.25% APR and another $2,000.00 in an account with an interest ra
Mila [183]
First account
interest = 6/12 × 5.25% × 4,000
interest = 1/2 × 5.25/100 × 4,000
interest = 1/2 × 210
interest = 105 dollars

Second account
interest = 6/12 × 6% × 2,000
interest = 1/2 × 6/100 × 2,000
interest = 1/2 × 120
interest = 60 dollars

After 6 months, the first account will have earned more interest than the second account
7 0
3 years ago
A metallurgist has an alloy with 5% titanium and an alloy with 30% titanium. He needs 100 grams of an alloy with 15% titanium. H
andrey2020 [161]
Let us convert the percentages to decimal format first.. so 5% is just 5/100 or 0.05 and 15% is just 15/100 or 0.15

so hmmm, so, let's say it needs "x" amount and "y" amount of each respectively, so, whatever "x" and "y" are, they must add up to 100, and whatever their concentration is, must add up to what the mixture yields

thus

\bf \begin{array}{lccclll}
&amount&concentration&
\begin{array}{llll}
concentrated\\
amount
\end{array}\\
&-----&-------&-------\\
\textit{5\% alloy}&x&0.05&0.05x\\
\textit{30\% alloy}&y&0.30&0.3y\\
-----&-----&-------&-------\\
mixture&100&0.15&15
\end{array}
\\\\\\
\begin{cases}
x+y=100\implies \boxed{y}=100-x\\
0.05x+0.3y=15\\
----------\\
0.5x+0.3\left( \boxed{100-x} \right)=15
\end{cases}

solve for "x"

what's "y"? well, y = 100 - x
4 0
3 years ago
Scientist are studying a bacteria sample. The function f(x)=360(1.07)^x gives the number of bacteria in the sample at the end of
Lapatulllka [165]

Options :

A. The initial number of bacteria is 7.

B. The initial of bacteria decreases at a rate of 93% each day.

C. The number of bacteria increases at a rate of 7% each day.

D. The number of bacteria at the end of one day is 360.

Answer:

C. The number of bacteria increases at a rate of 7% each day.

Step-by-step explanation:

Given the function :

f(x)=360(1.07)^x ; Number of bacteria in sample at the end of x days :

The function above represents an exponential growth function :

With the general form ; Ab^x

Where A = initial amount ;

b = growth rate

x = time

For the function :

A = initial amount of bacteria = 360

b = growth rate = (1 + r) = 1.07

If ; (1 + r) = 1.07 ; we can solve for r to obtain the daily growth rate ;

1 + r = 1.07

r = 1.07 - 1

r = 0.07

r as a percentage ;

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7 0
2 years ago
This puzzle is relatively easy, I just posted here cause I wanted to see if how many people can solve it. I capitalized some of
aleksandrvk [35]

Answer:

4 minutes

Step-by-step explanation:

2 will cook together for 1 minute. and it will take an additional 2 minutes to cook the 3rd pancake.

6 0
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