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vazorg [7]
3 years ago
12

Given that x is a normally distributed random variable with a mean of 50 and a standard deviation of 2, find the probability tha

t x is between 47 and 54.
Mathematics
1 answer:
Shkiper50 [21]3 years ago
5 0

Let X be the normal variable with mean μ =50 and standard deviation σ =2

We have to find probability that x is between 47 and 54

P(47 < X < 54) = P(X < 54) - P(X < 47)

= P(\frac{x-mean}{standard deviation} - P(\frac{x-mean}{standard deviation}

= P(Z < 2) - P(Z < -1.5)

Using standard normal z score table to find probabilities we get

P(Z < 2) = 0.9772

P(Z < -1.5) = 0.0668

P(47 < X < 54) = P(Z < 2) - P(Z < -1.5)

= 0.9772 - 0.0668

P(47 < X < 54) = 0.9104

The probability that x is between 47 and 54 is 0.9104

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Step-by-step explanation:

Given

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What is 3/7 plus 3/5 in fraction form?
Gnom [1K]
Least Common Factor(LCM) of 5 and 7: 35

7*5=35
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2 years ago
The football team need to buy Gatorade for Saturdays big game . They have two option. The first option us they can buy it pre-ma
VashaNatasha [74]

The question is incomplete. Here is the complete question.

The football team needed to buy Gatorade for Saturday's big game. They have two options. The first option is they can buy it pre-made in 48 ounces bottles for $3.84 for each bottle. Or they can buy packets and mix with water. Each packet makes 64 ounces and will cost $4.80.

a) Find the cost per ounce of each.

b) Which size costs less?

c) The team will need to buy 192 ounces of Gatorade. How much do you save using the choice from answer b?

Answer: a) Pre-made: $0.08 cost per ounce; Packet: $0.075 cost per ounce

              b) Packets

              c) Save $0.96.

Step-by-step explanation:

a) Cost per ounce:

<u>Pre-made:</u>

\frac{3.84}{48} = 0.08

<u>Packet:</u>

<u />\frac{4.8}{64} = 0.075

b) Comparing costs per ounce, packets costs less than pre-made.

c) Buying packets, the cost will be:

0.075*192 = $14.4

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0.08*192 = $15.36

Comparing costs, pre-made is 0.96 more than packets, so <u>they will save </u><u>96 cents</u>.

4 0
3 years ago
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