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shtirl [24]
3 years ago
8

The number of hours spent per week on household chores by all adults has a mean of 28 hours and a standard deviation of 7 hours.

The probability that the mean hours spent per week on household chores by a sample of 49 adults will be more than 26.75 is:
Mathematics
2 answers:
Alchen [17]3 years ago
4 0

Answer:

Probability that the mean hours spent per week on household chores by a sample of 49 adults will be more than 26.75 is 0.89435.

Step-by-step explanation:

We are given that the number of hours spent per week on household chores by all adults has a mean of 28 hours and a standard deviation of 7 hours.

Also, sample of 49 adults is given.

<em>Let X = number of hours spent per week on household chores</em>

So, assuming data follows normal distribution; X ~ N(\mu=28,\sigma^{2}=7^{2})

The z score probability distribution for sample mean is given by;

               Z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

where, \mu = mean hours = 28

            \sigma = standard deviation = 7 hours

            n = sample of adults = 49

<em>Let </em>\bar X<em> = sample mean hours spent per week on household chores</em>

So, probability that the mean hours spent per week on household chores by a sample of 49 adults will be more than 26.75 is given by =P(\bar X > 26.75 hours)

    P(\bar X > 26.75 hours) = P( \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } } > \frac{26.75-28}{\frac{7}{\sqrt{49} } } ) = P(Z > -1.25) = P(Z < 1.25)

                                                                     = 0.89435  {using z table}

Therefore, probability that the mean hours spent per week on household chores is more than 26.75 is 0.89435.

Ksivusya [100]3 years ago
4 0

Answer:

0.89435

Step-by-step explanation:

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